--- hol88-2.02.19940316.orig/Makefile
+++ hol88-2.02.19940316/Makefile
@@ -150,7 +150,7 @@
 
 LispType=cl
 Obj=o
-Lisp=akcl
+Lisp=gcl
 Liszt=
 LisztComm=
 Allegro=(set-case-mode :case-insensitive-upper)
@@ -159,7 +159,7 @@
 AllegroV4.1= $(AllegroV4.0) (setq *enable-package-locked-errors* nil)
 AllegroStuff= (progn () $(AllegroV4.1))
 
-HOLdir=/usr/local/hol
+HOLdir=$(shell pwd)
 Theory=$(HOLdir)/theories
 Library=$(HOLdir)/Library
 Help=$(HOLdir)/help/ENTRIES/
@@ -168,7 +168,7 @@
 LispDir=${HOLdir}/lisp
 
 ExeName = hol
-Version = 2.02 (SUN4/AKCL)
+Version = 2.02 (GCL)
 
 # =====================================================================
 # Default (from Phil Windley)
@@ -221,6 +221,34 @@
 # ---------------------------------------------------------------------
 
 hol: basic-hol ${Theory}/HOL.th $(HolMl) lisp/banner.$(Obj) lisp/akcl.l
+#	echo 'set_search_path[``; `${Theory}/`];;'\
+#	     'load_theory `HOL`;;'\
+#	     'loadf `ml/load_thms`;;'\
+#	     'loadf `ml/lib_loader`;;'\
+#	     'loadf `ml/numconv`;;'\
+#	     'loadf `ml/tydefs`;;'\
+#	     'loadf `ml/ind`;;'\
+#	     'loadf `ml/prim_rec`;;'\
+#	     'loadf `ml/tyfns`;;'\
+#	     'loadf `ml/num`;;'\
+#	     'loadf `ml/list`;;'\
+#	     'map delete_cache [`arithmetic`;`sum`;`list`];;'\
+#	     'map delete_cache [`tree`;`ltree`;`prim_rec`];;'\
+#	     'lisp `(load "lisp/banner")`;;'\
+#	     'lisp `(setq %system-name "HOL")`;;'\
+#	     'lisp `(setq %hol-dir "$(HOLdir)")`;;'\
+#	     'lisp `(setq %lib-dir "$(Library)")`;;'\
+#	     'lisp `(setq %liszt "$(LisztComm)")`;;'\
+#	     'lisp `(setq %version "$(Version)")`;;'\
+#	     'set_flag(`abort_when_fail`,false);;'\
+#	     'set_search_path[``; `~/`; `${Theory}/`];;'\
+#	     'set_help_search_path (words `$(Help)`);;'\
+#	     'set_library_search_path [`${Library}/`];;'\
+#	     'lisp `(setup)`;;'\
+#	     'save `${ExeName}`;;'\
+#	     'set_thm_count 0;;'\
+#	     'quit();;'\
+#	     | basic-hol
 	echo 'set_search_path[``; `${Theory}/`];;'\
 	     'load_theory `HOL`;;'\
 	     'loadf `ml/load_thms`;;'\
@@ -244,12 +272,8 @@
 	     'set_search_path[``; `~/`; `${Theory}/`];;'\
 	     'set_help_search_path (words `$(Help)`);;'\
 	     'set_library_search_path [`${Library}/`];;'\
-	     'lisp `(load "lisp/akcl.l")`;;'\
-	     'lisp `(setup)`;;'\
-	     'save `${ExeName}`;;'\
-	     'set_thm_count 0;;'\
-	     'quit();;'\
-	     | basic-hol
+	     'lisp `(setup)`;;' >foo2
+	     echo 'lisp `(throw (quote eof) t)`;; #+native-reloc(progn (with-open-file (s "foo2") (let ((*standard-input* s)) (tml)))(ml-save "hol")) #-native-reloc(let ((si::*collect-binary-modules* t)(si::*binary-modules* (with-open-file (s "bm.l") (read s)))) (with-open-file (s "foo2") (let ((*standard-input* s)) (tml)))(compiler::link (remove-duplicates si::*binary-modules* :test (function equal)) "hol" "(progn (load \"debian/gcl_patch.l\")(load \"foo\")(with-open-file (s \"foo1\") (let ((*standard-input* s)) (tml)))(with-open-file (s \"foo2\") (let ((*standard-input* s)) (tml)))(ml-save \"hol\")(quit))" "" nil)(quit))`;;' | basic-hol
 	make permissions
 	@echo "=======> hol88 version $(Version) made"
 
@@ -291,11 +315,12 @@
      Manual/Reference/bin/mktex Manual/Reference/bin/typecheck
 
 permissions:
-	find . \( -type d -user $(USER) -exec chmod $(Dperm) {} \; \) -o\
-	       \( -type f -user $(USER) -exec chmod $(Tperm) {} \; \)
-	@for f in $(Exec) ; do\
-	  ( if [ -f $$f ]; then\
-	    find $$f \( -user $(USER) \) -exec chmod $(Eperm) {} \; ;fi) ; \
+	find $$(ls -1 | grep -v debian) \
+	       \( -type d -exec chmod $(Dperm) {} \; \) -o\
+	       \( -type f -exec chmod $(Tperm) {} \; \)
+	for f in $(Exec) ; do\
+	  ( if [ -f $$f ] ; then\
+	    find $$f -exec chmod $(Eperm) {} \; ;fi) ; \
 	done
 
 
@@ -482,6 +507,31 @@
 # ---------------------------------------------------------------------
 
 basic-hol: hol-lcf $(BasicHolLisp) ${Theory}/BASIC-HOL.th $(BasicHolMl)
+#	echo 'set_search_path[``; `${Theory}/`];;'\
+#	     'load_theory `BASIC-HOL`;;'\
+#	     'loadf `ml/hol-in-out`;;'\
+#	     'loadf `ml/hol-rule`;;'\
+#	     'loadf `ml/hol-drule`;;'\
+#	     'loadf `ml/drul`;;'\
+#	     'loadf `ml/tacticals`;;'\
+#	     'loadf `ml/tacont`;;'\
+#	     'loadf `ml/tactics`;;'\
+#	     'loadf `ml/conv`;;'\
+#	     'loadf `ml/hol-net`;;'\
+#	     'loadf `ml/rewrite`;;'\
+#	     'loadf `ml/resolve`;;'\
+#	     'loadf `ml/hol-thyfn`;;'\
+#	     'loadf `ml/goals`;;'\
+#	     'loadf `ml/stack`;;'\
+#	     'loadf `ml/abs-rep`;;'\
+#             'activate_binders `bool`;;'\
+#	     'lisp `(setq %liszt "$(LisztComm)")`;;'\
+#	     'lisp `(setq %version "$(Version)")`;;'\
+#	     'lisp `(setq %system-name "BASIC-HOL")`;;'\
+#	     'lisp `(setup)`;;'\
+#	     'save `basic-hol`;;'\
+#	     'quit();;'\
+#	     | hol-lcf
 	echo 'set_search_path[``; `${Theory}/`];;'\
 	     'load_theory `BASIC-HOL`;;'\
 	     'loadf `ml/hol-in-out`;;'\
@@ -503,10 +553,8 @@
 	     'lisp `(setq %liszt "$(LisztComm)")`;;'\
 	     'lisp `(setq %version "$(Version)")`;;'\
 	     'lisp `(setq %system-name "BASIC-HOL")`;;'\
-	     'lisp `(setup)`;;'\
-	     'save `basic-hol`;;'\
-	     'quit();;'\
-	     | hol-lcf
+	     'lisp `(setup)`;;' >foo1
+	     echo 'lisp `(throw (quote eof) t)`;; #+native-reloc(progn (with-open-file (s "foo1") (let ((*standard-input* s)) (tml)))(ml-save "basic-hol")) #-native-reloc(let ((si::*collect-binary-modules* t)(si::*binary-modules* (with-open-file (s "bm.l") (read s)))) (with-open-file (s "foo1") (let ((*standard-input* s)) (tml)))(compiler::link (remove-duplicates si::*binary-modules* :test (function equal)) "basic-hol" "(progn (load \"debian/gcl_patch.l\")(load \"foo\")(with-open-file (s \"foo1\") (let ((*standard-input* s)) (tml)))(ml-save \"basic-hol\")(quit))" "" nil)(with-open-file (s "bm.l" :direction :output) (prin1 si::*binary-modules* s))(quit))`;;' | hol-lcf
 	@echo "=======> basic-hol88 made"
 
 # ---------------------------------------------------------------------
@@ -780,6 +828,23 @@
 # ---------------------------------------------------------------------
 
 hol-lcf: $(HolLcfLisp) $(HolLcfMl)
+#	echo '#+allegro $(AllegroStuff)'\
+#	     '(load "lisp/mk-ml")'\
+#	     '(load "lisp/mk-hol-lcf")'\
+#	     '(setq %version "$(Version)")'\
+#	     '(set-make)'\
+#	     '(tml)'\
+#	     'load(`ml/site`,false);;'\
+#	     'load(`ml/ml-curry`,false);;'\
+#	     'load(`ml/lis`,false);;'\
+#	     'load(`ml/gen`,false);;'\
+#	     'load(`ml/killpp`,false);;'\
+#	     'lisp `(setq %system-name "HOL-LCF")`;;'\
+#	     'lisp `(setq %liszt "$(LisztComm)")`;;'\
+#	     'lisp `(setup)`;;'\
+#	     'save `hol-lcf`;;'\
+#	     'quit();;'\
+#	     | $(Lisp)
 	echo '#+allegro $(AllegroStuff)'\
 	     '(load "lisp/mk-ml")'\
 	     '(load "lisp/mk-hol-lcf")'\
@@ -793,10 +858,8 @@
 	     'load(`ml/killpp`,false);;'\
 	     'lisp `(setq %system-name "HOL-LCF")`;;'\
 	     'lisp `(setq %liszt "$(LisztComm)")`;;'\
-	     'lisp `(setup)`;;'\
-	     'save `hol-lcf`;;'\
-	     'quit();;'\
-	     | $(Lisp)
+	     'lisp `(setup)`;;' >foo
+	echo '#+native-reloc(progn (load "foo")(ml-save "hol-lcf"))#-native-reloc(let ((si::*collect-binary-modules* t)(si::*binary-modules* nil)) (load "foo")(compiler::link (remove-duplicates si::*binary-modules* :test (function equal)) "hol-lcf" "(load \"debian/gcl_patch.l\")(load \"foo\")(ml-save \"hol-lcf\")" "" nil)(with-open-file (s "bm.l" :direction :output) (prin1 si::*binary-modules* s)))(quit)' | $(Lisp)
 	@echo "=======> hol-lcf made"
 
 # =====================================================================
--- hol88-2.02.19940316.orig/Library/more_arithmetic/Manual/entries.tex
+++ hol88-2.02.19940316/Library/more_arithmetic/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the more\_arithmetic Library}
-\input{entries-intro}
-\DOC{GEN\_INDUCT\_RULE}
+\chapter{ML Functions in the more\_arithmetic Library}\input{entries-intro}\DOC{GEN\_INDUCT\_RULE}
 
 \TYPE {\small\verb%GEN_INDUCT_RULE : (thm -> thm -> thm)%}\egroup
 
--- hol88-2.02.19940316.orig/Library/more_arithmetic/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/more_arithmetic/Manual/theorems.tex
@@ -1,7 +1,4 @@
-\chapter{Pre-proved Theorems}\label{thms}
-\input{theorems-intro}
-\section{Theorems about Inequalities}
-\THEOREM GEN\_INDUCTION ineq
+\chapter{Pre-proved Theorems}\label{thms}\input{theorems-intro}\section{Theorems about Inequalities}\THEOREM GEN\_INDUCTION ineq
 |- !P. P 0 /\ (!n. (!m. m < n ==> P m) ==> P n) ==> (!n. P n)
 \ENDTHEOREM
 \THEOREM GREATER\_EQ\_ANTISYM ineq
@@ -19,8 +16,7 @@
 \THEOREM NOT\_LESS\_AND\_GREATER ineq
 |- !n m. n < m ==> ~m < n
 \ENDTHEOREM
-\section{Theorems about {\tt 0}}
-\THEOREM GREATER\_NOT\_ZERO zero\_ineq
+\section{Theorems about {\tt 0}}\THEOREM GREATER\_NOT\_ZERO zero\_ineq
 |- !x. 0 < x ==> ~(x = 0)
 \ENDTHEOREM
 \THEOREM LESS1EQ0 zero\_ineq
@@ -38,8 +34,7 @@
 \THEOREM NOT\_EQ\_0 zero\_ineq
 |- !m. ~(m = 0) ==> m >= 1
 \ENDTHEOREM
-\section{Theorems about {\tt SUC}}
-\THEOREM LESS\_EQ\_LESS\_SUC suc
+\section{Theorems about {\tt SUC}}\THEOREM LESS\_EQ\_LESS\_SUC suc
 |- !m n. m <= n = m < (SUC n)
 \ENDTHEOREM
 \THEOREM NOT\_0\_GREATER\_EQ\_SUC suc
@@ -63,8 +58,7 @@
 \THEOREM SUC\_NOT\_0 suc
 |- !n. ~(SUC n = 0)
 \ENDTHEOREM
-\section{Theorems about {\tt PRE}}
-\THEOREM LESS\_IMP\_LESS\_EQ\_PRE pre
+\section{Theorems about {\tt PRE}}\THEOREM LESS\_IMP\_LESS\_EQ\_PRE pre
 |- !m n. 0 < n ==> (m < n = m <= (PRE n))
 \ENDTHEOREM
 \THEOREM PRE\_ADD pre
@@ -94,31 +88,30 @@
 \THEOREM SUC\_PRE pre
 |- !n. 0 < n ==> (SUC(PRE n) = n)
 \ENDTHEOREM
-\section{Theorems about Addition}
+\section{Theorems about Addition}\THEOREM ADD\_EQ\_LESS\_EQ add
+|- !m n p. (m + n = p) ==> m <= p
+\ENDTHEOREM
+\THEOREM ADD\_EQ\_LESS\_IMP\_LESS add
+|- !n m k l. (k + m = l + n) /\ k < l ==> n < m
+\ENDTHEOREM
+\THEOREM ADD\_GREATER\_EQ add
+|- !m n. (m + n) >= m
+\ENDTHEOREM
 \THEOREM ADDL\_GREATER add
 |- !m n p. m < n ==> m < (p + n)
 \ENDTHEOREM
 \THEOREM ADDL\_GREATER\_EQ add
 |- !m n p. m <= n ==> m <= (p + n)
 \ENDTHEOREM
+\THEOREM ADD\_MONO\_LESS add
+|- !m n p. (m + p) < (m + n) = p < n
+\ENDTHEOREM
 \THEOREM ADDR\_GREATER add
 |- !m n p. m < n ==> m < (n + p)
 \ENDTHEOREM
 \THEOREM ADDR\_GREATER\_EQ add
 |- !m n p. m <= n ==> m <= (n + p)
 \ENDTHEOREM
-\THEOREM ADD\_EQ\_LESS\_EQ add
-|- !m n p. (m + n = p) ==> m <= p
-\ENDTHEOREM
-\THEOREM ADD\_EQ\_LESS\_IMP\_LESS add
-|- !n m k l. (k + m = l + n) /\ k < l ==> n < m
-\ENDTHEOREM
-\THEOREM ADD\_GREATER\_EQ add
-|- !m n. (m + n) >= m
-\ENDTHEOREM
-\THEOREM ADD\_MONO\_LESS add
-|- !m n p. (m + p) < (m + n) = p < n
-\ENDTHEOREM
 \THEOREM ADD\_SUC\_0 add
 |- !m. SUC m = (SUC 0) + m
 \ENDTHEOREM
@@ -174,8 +167,7 @@
 \THEOREM SUM\_LESS add
 |- !m n p. (m + n) < p ==> m < p /\ n < p
 \ENDTHEOREM
-\section{Theorems about Subtraction}
-\THEOREM ADD\_EQ\_IMP\_SUB\_EQ sub
+\section{Theorems about Subtraction}\THEOREM ADD\_EQ\_IMP\_SUB\_EQ sub
 |- !a b c. (a = b + c) ==> (a - b = c)
 \ENDTHEOREM
 \THEOREM ADD\_LESS\_EQ\_SUB sub
@@ -253,6 +245,9 @@
 \THEOREM SUB\_GREATER\_EQ\_ADD sub
 |- !n m p. p >= n ==> ((p - n) >= m = p >= (n + m))
 \ENDTHEOREM
+\THEOREM SUB\_LE\_ADD sub
+|- !n m p. n <= p ==> (m <= (p - n) = (n + m) <= p)
+\ENDTHEOREM
 \THEOREM SUB\_LESS\_BOTH\_SIDES sub
 |- !m n p. p <= m /\ m < n ==> (m - p) < (n - p)
 \ENDTHEOREM
@@ -268,9 +263,6 @@
 \THEOREM SUB\_LESS\_TO\_LESS\_ADDR sub
 |- !m n p. p <= m ==> ((m - p) < n = m < (n + p))
 \ENDTHEOREM
-\THEOREM SUB\_LE\_ADD sub
-|- !n m p. n <= p ==> (m <= (p - n) = (n + m) <= p)
-\ENDTHEOREM
 \THEOREM SUB\_PRE\_SUB\_1 sub
 |- !a b. 0 < b ==> ((a - (PRE b)) - 1 = a - b)
 \ENDTHEOREM
@@ -288,8 +280,7 @@
     (m < n ==> ((SUC m) - n = 0)) /\
     (~m < n ==> ((SUC m) - n = SUC(m - n)))
 \ENDTHEOREM
-\section{Theorems about Multiplication and Exponential Functions}
-\THEOREM EXP1 mult
+\section{Theorems about Multiplication and Exponential Functions}\THEOREM EXP1 mult
 |- !n. n EXP 1 = n
 \ENDTHEOREM
 \THEOREM LESS\_MONO\_MULT1 mult
@@ -310,8 +301,7 @@
 \THEOREM ZERO\_LESS\_TWO\_EXP mult
 |- !n. 0 < (2 EXP n)
 \ENDTHEOREM
-\section{Theorems about Division}
-\THEOREM ADD\_DIV\_ADD\_DIV div\_mod
+\section{Theorems about Division}\THEOREM ADD\_DIV\_ADD\_DIV div\_mod
 |- !n. 0 < n ==> (!x r. ((x * n) + r) DIV n = x + (r DIV n))
 \ENDTHEOREM
 \THEOREM ADD\_DIV\_SUC\_DIV div\_mod
@@ -349,8 +339,7 @@
 \THEOREM SUC\_MOD\_SELF div\_mod
 |- !n. (SUC n) MOD (SUC n) = 0
 \ENDTHEOREM
-\section{Theorems about Maximum and Minimum}
-\THEOREM MAX\_0 min\_max
+\section{Theorems about Maximum and Minimum}\THEOREM MAX\_0 min\_max
 |- !n. MAX 0 n = n
 \ENDTHEOREM
 \THEOREM MAX\_DEF min\_max
@@ -386,8 +375,7 @@
 \THEOREM SUC\_MIN min\_max
 |- !n p. MIN(SUC n)(SUC p) = SUC(MIN n p)
 \ENDTHEOREM
-\section{Theorems about Odd and Even Numbers}
-\THEOREM EVEN\_MULT odd\_even
+\section{Theorems about Odd and Even Numbers}\THEOREM EVEN\_MULT odd\_even
 |- !n m. EVEN n \/ EVEN m ==> EVEN(n * m)
 \ENDTHEOREM
 \THEOREM EVEN\_ODD\_0 odd\_even
--- hol88-2.02.19940316.orig/Library/sets/Manual/entries.tex
+++ hol88-2.02.19940316/Library/sets/Manual/entries.tex
@@ -1,7 +1,4 @@
-\chapter{ML Functions in the sets Library}
-\label{entries}
-\input{entries-intro}
-\DOC{DELETE\_CONV}
+\chapter{ML Functions in the sets Library}\label{entries}\input{entries-intro}\DOC{DELETE\_CONV}
 
 \TYPE {\small\verb%DELETE_CONV : conv -> conv%}\egroup
 
@@ -204,6 +201,84 @@
 
 \ENDDOC
 
+\DOC{IN\_CONV}
+
+\TYPE {\small\verb%IN_CONV : conv -> conv%}\egroup
+
+\SYNOPSIS
+Decision procedure for membership in finite sets.
+
+\DESCRIBE 
+The function {\small\verb%IN_CONV%} is a parameterized conversion for proving or disproving
+membership assertions of the general form:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   "t IN {t1,...,tn}"
+\end{verbatim}
+}
+\noindent where {\small\verb%{t1,...,tn}%} is a set of type {\small\verb%(ty)set%} and {\small\verb%t%} is a value
+of the base type {\small\verb%ty%}.  The first argument to {\small\verb%IN_CONV%} is expected to be a
+conversion that decides equality between values of the base type {\small\verb%ty%}.  Given
+an equation {\small\verb%"e1 = e2"%}, where {\small\verb%e1%} and {\small\verb%e2%} are terms of type {\small\verb%ty%}, this
+conversion should return the theorem {\small\verb%|- (e1 = e2) = T%} or the theorem
+{\small\verb%|- (e1 = e2) = F%}, as appropriate.
+
+Given such a conversion, the function {\small\verb%IN_CONV%} returns a conversion that
+maps a term of the form {\small\verb%"t IN {t1,...,tn}"%} to the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- t IN {t1,...,tn} = T
+\end{verbatim}
+}
+
+\noindent if {\small\verb%t%} is alpha-equivalent to any {\small\verb%ti%}, or if the supplied conversion
+proves {\small\verb%|- (t = ti) = T%} for any {\small\verb%ti%}. If the supplied conversion proves
+{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}, then the result is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- t IN {t1,...,tn} = F 
+\end{verbatim}
+}
+\noindent In all other cases, {\small\verb%IN_CONV%} will fail.
+
+\EXAMPLE
+In the following example, the conversion {\small\verb%num_EQ_CONV%} is supplied as a
+parameter and used to test equality of the candidate element {\small\verb%1%} with the
+actual elements of the given set.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV num_EQ_CONV "2 IN {0,SUC 1,3}";;
+   |- 2 IN {0,SUC 1,3} = T
+\end{verbatim}
+}
+\noindent The result is {\small\verb%T%} because {\small\verb%num_EQ_CONV%} is able to prove that {\small\verb%2%} is
+equal to {\small\verb%SUC 1%}. An example of a negative result is:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV num_EQ_CONV "1 IN {0,2,3}";;
+   |- 1 IN {0,2,3} = F
+\end{verbatim}
+}
+\noindent Finally the behaviour of the supplied conversion is irrelevant when
+the value to be tested for membership is alpha-equivalent to an actual element:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV NO_CONV "1 IN {3,2,1}";;
+   |- 1 IN {3,2,1} = T
+\end{verbatim}
+}
+\noindent The conversion {\small\verb%NO_CONV%} always fails, but {\small\verb%IN_CONV%} is nontheless
+able in this case to prove the required result.
+
+\FAILURE
+{\small\verb%IN_CONV conv%} fails if applied to a term that is not of the form {\small\verb%"t IN
+{t1,...,tn}"%}.  A call {\small\verb%IN_CONV conv "t IN {t1,...,tn}"%} fails unless the
+term {\small\verb%t%} is alpha-equivalent to some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
+{\small\verb%|- (t = ti) = T%} for some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
+{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}.
+
+\ENDDOC
+
 \DOC{INSERT\_CONV}
 
 \TYPE {\small\verb%INSERT_CONV : conv -> conv%}\egroup
@@ -290,84 +365,6 @@
 
 \ENDDOC
 
-\DOC{IN\_CONV}
-
-\TYPE {\small\verb%IN_CONV : conv -> conv%}\egroup
-
-\SYNOPSIS
-Decision procedure for membership in finite sets.
-
-\DESCRIBE 
-The function {\small\verb%IN_CONV%} is a parameterized conversion for proving or disproving
-membership assertions of the general form:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   "t IN {t1,...,tn}"
-\end{verbatim}
-}
-\noindent where {\small\verb%{t1,...,tn}%} is a set of type {\small\verb%(ty)set%} and {\small\verb%t%} is a value
-of the base type {\small\verb%ty%}.  The first argument to {\small\verb%IN_CONV%} is expected to be a
-conversion that decides equality between values of the base type {\small\verb%ty%}.  Given
-an equation {\small\verb%"e1 = e2"%}, where {\small\verb%e1%} and {\small\verb%e2%} are terms of type {\small\verb%ty%}, this
-conversion should return the theorem {\small\verb%|- (e1 = e2) = T%} or the theorem
-{\small\verb%|- (e1 = e2) = F%}, as appropriate.
-
-Given such a conversion, the function {\small\verb%IN_CONV%} returns a conversion that
-maps a term of the form {\small\verb%"t IN {t1,...,tn}"%} to the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- t IN {t1,...,tn} = T
-\end{verbatim}
-}
-
-\noindent if {\small\verb%t%} is alpha-equivalent to any {\small\verb%ti%}, or if the supplied conversion
-proves {\small\verb%|- (t = ti) = T%} for any {\small\verb%ti%}. If the supplied conversion proves
-{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}, then the result is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- t IN {t1,...,tn} = F 
-\end{verbatim}
-}
-\noindent In all other cases, {\small\verb%IN_CONV%} will fail.
-
-\EXAMPLE
-In the following example, the conversion {\small\verb%num_EQ_CONV%} is supplied as a
-parameter and used to test equality of the candidate element {\small\verb%1%} with the
-actual elements of the given set.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV num_EQ_CONV "2 IN {0,SUC 1,3}";;
-   |- 2 IN {0,SUC 1,3} = T
-\end{verbatim}
-}
-\noindent The result is {\small\verb%T%} because {\small\verb%num_EQ_CONV%} is able to prove that {\small\verb%2%} is
-equal to {\small\verb%SUC 1%}. An example of a negative result is:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV num_EQ_CONV "1 IN {0,2,3}";;
-   |- 1 IN {0,2,3} = F
-\end{verbatim}
-}
-\noindent Finally the behaviour of the supplied conversion is irrelevant when
-the value to be tested for membership is alpha-equivalent to an actual element:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV NO_CONV "1 IN {3,2,1}";;
-   |- 1 IN {3,2,1} = T
-\end{verbatim}
-}
-\noindent The conversion {\small\verb%NO_CONV%} always fails, but {\small\verb%IN_CONV%} is nontheless
-able in this case to prove the required result.
-
-\FAILURE
-{\small\verb%IN_CONV conv%} fails if applied to a term that is not of the form {\small\verb%"t IN
-{t1,...,tn}"%}.  A call {\small\verb%IN_CONV conv "t IN {t1,...,tn}"%} fails unless the
-term {\small\verb%t%} is alpha-equivalent to some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
-{\small\verb%|- (t = ti) = T%} for some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
-{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}.
-
-\ENDDOC
-
 \DOC{SET\_INDUCT\_TAC}
 
 \TYPE {\small\verb%SET_INDUCT_TAC : tactic%}\egroup
--- hol88-2.02.19940316.orig/Library/sets/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/sets/Manual/theorems.tex
@@ -1,22 +1,18 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{The type definition}
-\THEOREM set\_ISO\_DEF sets
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{The type definition}\THEOREM set\_ISO\_DEF sets
 |- (!a. SPEC(CHF a) = a) /\ (!r. (\p. T)r = (CHF(SPEC r) = r))
 \ENDTHEOREM
 \THEOREM set\_TY\_DEF sets
 |- ?rep. TYPE_DEFINITION(\p. T)rep
 \ENDTHEOREM
-\section{Membership, equality, and set specifications}
-\THEOREM EXTENSION sets
+\section{Membership, equality, and set specifications}\THEOREM EXTENSION sets
 |- !s t. (s = t) = (!x. x IN s = x IN t)
 \ENDTHEOREM
-\THEOREM GSPECIFICATION sets
-|- !f v. v IN (GSPEC f) = (?x. v,T = f x)
-\ENDTHEOREM
 \THEOREM GSPEC\_DEF sets
 |- !f. GSPEC f = SPEC(\y. ?x. y,T = f x)
 \ENDTHEOREM
+\THEOREM GSPECIFICATION sets
+|- !f v. v IN (GSPEC f) = (?x. v,T = f x)
+\ENDTHEOREM
 \THEOREM IN\_DEF sets
 |- !x s. x IN s = CHF s x
 \ENDTHEOREM
@@ -32,8 +28,7 @@
 \THEOREM SPECIFICATION sets
 |- !P x. x IN (SPEC P) = P x
 \ENDTHEOREM
-\section{The empty and universal sets}
-\THEOREM EMPTY\_DEF sets
+\section{The empty and universal sets}\THEOREM EMPTY\_DEF sets
 |- {} = SPEC(\x. F)
 \ENDTHEOREM
 \THEOREM EMPTY\_NOT\_UNIV sets
@@ -57,8 +52,7 @@
 \THEOREM UNIV\_NOT\_EMPTY sets
 |- ~(UNIV = {})
 \ENDTHEOREM
-\section{Set inclusion}
-\THEOREM EMPTY\_SUBSET sets
+\section{Set inclusion}\THEOREM EMPTY\_SUBSET sets
 |- !s. {} SUBSET s
 \ENDTHEOREM
 \THEOREM NOT\_PSUBSET\_EMPTY sets
@@ -103,10 +97,12 @@
 \THEOREM UNIV\_SUBSET sets
 |- !s. UNIV SUBSET s = (s = UNIV)
 \ENDTHEOREM
-\section{Intersection and union}
-\THEOREM EMPTY\_UNION sets
+\section{Intersection and union}\THEOREM EMPTY\_UNION sets
 |- !s t. (s UNION t = {}) = (s = {}) /\ (t = {})
 \ENDTHEOREM
+\THEOREM IN\_INTER sets
+|- !s t x. x IN (s INTER t) = x IN s /\ x IN t
+\ENDTHEOREM
 \THEOREM INTER\_ASSOC sets
 |- !s t u. (s INTER t) INTER u = s INTER (t INTER u)
 \ENDTHEOREM
@@ -131,21 +127,18 @@
 \THEOREM INTER\_UNIV sets
 |- (!s. UNIV INTER s = s) /\ (!s. s INTER UNIV = s)
 \ENDTHEOREM
-\THEOREM IN\_INTER sets
-|- !s t x. x IN (s INTER t) = x IN s /\ x IN t
-\ENDTHEOREM
 \THEOREM IN\_UNION sets
 |- !s t x. x IN (s UNION t) = x IN s \/ x IN t
 \ENDTHEOREM
 \THEOREM SUBSET\_INTER\_ABSORPTION sets
 |- !s t. s SUBSET t = (s INTER t = s)
 \ENDTHEOREM
-\THEOREM SUBSET\_UNION sets
-|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
-\ENDTHEOREM
 \THEOREM SUBSET\_UNION\_ABSORPTION sets
 |- !s t. s SUBSET t = (s UNION t = t)
 \ENDTHEOREM
+\THEOREM SUBSET\_UNION sets
+|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
+\ENDTHEOREM
 \THEOREM UNION\_ASSOC sets
 |- !s t u. (s UNION t) UNION u = s UNION (t UNION u)
 \ENDTHEOREM
@@ -167,8 +160,7 @@
 \THEOREM UNION\_UNIV sets
 |- (!s. UNIV UNION s = UNIV) /\ (!s. s UNION UNIV = UNIV)
 \ENDTHEOREM
-\section{Set difference}
-\THEOREM DIFF\_DEF sets
+\section{Set difference}\THEOREM DIFF\_DEF sets
 |- !s t. s DIFF t = {x | x IN s /\ ~x IN t}
 \ENDTHEOREM
 \THEOREM DIFF\_DIFF sets
@@ -189,8 +181,7 @@
 \THEOREM IN\_DIFF sets
 |- !s t x. x IN (s DIFF t) = x IN s /\ ~x IN t
 \ENDTHEOREM
-\section{Disjoint sets}
-\THEOREM DISJOINT\_DEF sets
+\section{Disjoint sets}\THEOREM DISJOINT\_DEF sets
 |- !s t. DISJOINT s t = (s INTER t = {})
 \ENDTHEOREM
 \THEOREM DISJOINT\_DELETE\_SYM sets
@@ -212,8 +203,7 @@
 \THEOREM IN\_DISJOINT sets
 |- !s t. DISJOINT s t = ~(?x. x IN s /\ x IN t)
 \ENDTHEOREM
-\section{Insertion and deletion of an element}
-\THEOREM ABSORPTION sets
+\section{Insertion and deletion of an element}\THEOREM ABSORPTION sets
 |- !x s. x IN s = (x INSERT s = s)
 \ENDTHEOREM
 \THEOREM COMPONENT sets
@@ -254,6 +244,16 @@
 \THEOREM EMPTY\_DELETE sets
 |- !x. {} DELETE x = {}
 \ENDTHEOREM
+\THEOREM IN\_DELETE sets
+|- !s x y. x IN (s DELETE y) = x IN s /\ ~(x = y)
+\ENDTHEOREM
+\THEOREM IN\_DELETE\_EQ sets
+|- !s x x'.
+    (x IN s = x' IN s) = (x IN (s DELETE x') = x' IN (s DELETE x))
+\ENDTHEOREM
+\THEOREM IN\_INSERT sets
+|- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
+\ENDTHEOREM
 \THEOREM INSERT\_COMM sets
 |- !x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)
 \ENDTHEOREM
@@ -287,16 +287,6 @@
 \THEOREM INSERT\_UNIV sets
 |- !x. x INSERT UNIV = UNIV
 \ENDTHEOREM
-\THEOREM IN\_DELETE sets
-|- !s x y. x IN (s DELETE y) = x IN s /\ ~(x = y)
-\ENDTHEOREM
-\THEOREM IN\_DELETE\_EQ sets
-|- !s x x'.
-    (x IN s = x' IN s) = (x IN (s DELETE x') = x' IN (s DELETE x))
-\ENDTHEOREM
-\THEOREM IN\_INSERT sets
-|- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
-\ENDTHEOREM
 \THEOREM NOT\_EMPTY\_INSERT sets
 |- !x s. ~({} = x INSERT s)
 \ENDTHEOREM
@@ -312,14 +302,13 @@
 \THEOREM SUBSET\_DELETE sets
 |- !x s t. s SUBSET (t DELETE x) = ~x IN s /\ s SUBSET t
 \ENDTHEOREM
-\THEOREM SUBSET\_INSERT sets
-|- !x s. ~x IN s ==> (!t. s SUBSET (x INSERT t) = s SUBSET t)
-\ENDTHEOREM
 \THEOREM SUBSET\_INSERT\_DELETE sets
 |- !x s t. s SUBSET (x INSERT t) = (s DELETE x) SUBSET t
 \ENDTHEOREM
-\section{The {\tt CHOICE} and {\tt REST} functions}
-\THEOREM CHOICE\_DEF sets
+\THEOREM SUBSET\_INSERT sets
+|- !x s. ~x IN s ==> (!t. s SUBSET (x INSERT t) = s SUBSET t)
+\ENDTHEOREM
+\section{The {\tt CHOICE} and {\tt REST} functions}\THEOREM CHOICE\_DEF sets
 |- !s. ~(s = {}) ==> (CHOICE s) IN s
 \ENDTHEOREM
 \THEOREM CHOICE\_INSERT\_REST sets
@@ -346,8 +335,7 @@
 \THEOREM SING\_IFF\_EMPTY\_REST sets
 |- !s. SING s = ~(s = {}) /\ (REST s = {})
 \ENDTHEOREM
-\section{Image of a function on a set}
-\THEOREM IMAGE\_COMPOSE sets
+\section{Image of a function on a set}\THEOREM IMAGE\_COMPOSE sets
 |- !f g s. IMAGE(f o g)s = IMAGE f(IMAGE g s)
 \ENDTHEOREM
 \THEOREM IMAGE\_DEF sets
@@ -383,8 +371,7 @@
 \THEOREM IN\_IMAGE sets
 |- !y s f. y IN (IMAGE f s) = (?x. (y = f x) /\ x IN s)
 \ENDTHEOREM
-\section{Mappings between sets}
-\THEOREM BIJ\_COMPOSE sets
+\section{Mappings between sets}\THEOREM BIJ\_COMPOSE sets
 |- !f g s t u. BIJ f s t /\ BIJ g t u ==> BIJ(g o f)s u
 \ENDTHEOREM
 \THEOREM BIJ\_DEF sets
@@ -435,8 +422,7 @@
 \THEOREM SURJ\_ID sets
 |- !s. SURJ(\x. x)s s
 \ENDTHEOREM
-\section{Singleton sets}
-\THEOREM DELETE\_EQ\_SING sets
+\section{Singleton sets}\THEOREM DELETE\_EQ\_SING sets
 |- !s x. x IN s ==> ((s DELETE x = {}) = (s = {x}))
 \ENDTHEOREM
 \THEOREM DISJOINT\_SING\_EMPTY sets
@@ -460,20 +446,19 @@
 \THEOREM NOT\_SING\_EMPTY sets
 |- !x. ~({x} = {})
 \ENDTHEOREM
-\THEOREM SING sets
-|- !x. SING{x}
-\ENDTHEOREM
 \THEOREM SING\_DEF sets
 |- !s. SING s = (?x. s = {x})
 \ENDTHEOREM
 \THEOREM SING\_DELETE sets
 |- !x. {x} DELETE x = {}
 \ENDTHEOREM
+\THEOREM SING sets
+|- !x. SING{x}
+\ENDTHEOREM
 \THEOREM SING\_FINITE sets
 |- !s. SING s ==> FINITE s
 \ENDTHEOREM
-\section{Finite and infinite sets}
-\THEOREM FINITE\_DEF sets
+\section{Finite and infinite sets}\THEOREM FINITE\_DEF sets
 |- !s.
     FINITE s = (!P. P{} /\ (!s'. P s' ==> (!e. P(e INSERT s'))) ==> P s)
 \ENDTHEOREM
@@ -531,12 +516,12 @@
 |- INFINITE (UNIV:(*)set) =
    (?f:*->*. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y)))
 \ENDTHEOREM
-\THEOREM INTER\_FINITE sets
-|- !s. FINITE s ==> (!t. FINITE(s INTER t))
-\ENDTHEOREM
 \THEOREM IN\_INFINITE\_NOT\_FINITE sets
 |- !s t. INFINITE s /\ FINITE t ==> (?x. x IN s /\ ~x IN t)
 \ENDTHEOREM
+\THEOREM INTER\_FINITE sets
+|- !s. FINITE s ==> (!t. FINITE(s INTER t))
+\ENDTHEOREM
 \THEOREM NOT\_IN\_FINITE sets
 |- INFINITE UNIV = (!s. FINITE s ==> (?x. ~x IN s))
 \ENDTHEOREM
@@ -546,8 +531,7 @@
 \THEOREM SUBSET\_FINITE sets
 |- !s. FINITE s ==> (!t. t SUBSET s ==> FINITE t)
 \ENDTHEOREM
-\section{Cardinality of sets}
-\THEOREM CARD\_DEF sets
+\section{Cardinality of sets}\THEOREM CARD\_DEF sets
 |- (CARD{} = 0) /\
    (!s.
      FINITE s ==>
--- hol88-2.02.19940316.orig/Library/trs/Manual/entries.tex
+++ hol88-2.02.19940316/Library/trs/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the trs Library}
-\input{entries-intro}
-\DOC{Ancestors}
+\chapter{ML Functions in the trs Library}\input{entries-intro}\DOC{Ancestors}
 
 \TYPE {\small\verb%Ancestors : ((string list # string list) -> searchpath)%}\egroup
 
--- hol88-2.02.19940316.orig/Library/reals/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/reals/Manual/theorems.tex
@@ -1,18 +1,15 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{HRAT}
-\THEOREM hrat\_1 HRAT
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{HRAT}\THEOREM hrat\_1 HRAT
 |- hrat_1 = mk_hrat($trat_eq trat_1)
 \ENDTHEOREM
+\THEOREM HRAT\_ADD\_ASSOC HRAT
+|- !h i j. h hrat_add (i hrat_add j) = (h hrat_add i) hrat_add j
+\ENDTHEOREM
 \THEOREM hrat\_add HRAT
 |- !g00014 g00015.
     g00014 hrat_add g00015 =
     mk_hrat
     ($trat_eq(($@(dest_hrat g00014)) trat_add ($@(dest_hrat g00015))))
 \ENDTHEOREM
-\THEOREM HRAT\_ADD\_ASSOC HRAT
-|- !h i j. h hrat_add (i hrat_add j) = (h hrat_add i) hrat_add j
-\ENDTHEOREM
 \THEOREM HRAT\_ADD\_SYM HRAT
 |- !h i. h hrat_add i = i hrat_add h
 \ENDTHEOREM
@@ -30,15 +27,15 @@
 |- !h i j.
     h hrat_mul (i hrat_add j) = (h hrat_mul i) hrat_add (h hrat_mul j)
 \ENDTHEOREM
+\THEOREM HRAT\_MUL\_ASSOC HRAT
+|- !h i j. h hrat_mul (i hrat_mul j) = (h hrat_mul i) hrat_mul j
+\ENDTHEOREM
 \THEOREM hrat\_mul HRAT
 |- !g00016 g00017.
     g00016 hrat_mul g00017 =
     mk_hrat
     ($trat_eq(($@(dest_hrat g00016)) trat_mul ($@(dest_hrat g00017))))
 \ENDTHEOREM
-\THEOREM HRAT\_MUL\_ASSOC HRAT
-|- !h i j. h hrat_mul (i hrat_mul j) = (h hrat_mul i) hrat_mul j
-\ENDTHEOREM
 \THEOREM HRAT\_MUL\_LID HRAT
 |- !h. hrat_1 hrat_mul h = h
 \ENDTHEOREM
@@ -51,13 +48,13 @@
 \THEOREM HRAT\_NOZERO HRAT
 |- !h i. ~(h hrat_add i = h)
 \ENDTHEOREM
+\THEOREM hrat\_sucint HRAT
+|- !g00018. hrat_sucint g00018 = mk_hrat($trat_eq(trat_sucint g00018))
+\ENDTHEOREM
 \THEOREM HRAT\_SUCINT HRAT
 |- (hrat_sucint 0 = hrat_1) /\
    (!n. hrat_sucint(SUC n) = (hrat_sucint n) hrat_add hrat_1)
 \ENDTHEOREM
-\THEOREM hrat\_sucint HRAT
-|- !g00018. hrat_sucint g00018 = mk_hrat($trat_eq(trat_sucint g00018))
-\ENDTHEOREM
 \THEOREM hrat\_tybij HRAT
 |- (!a. mk_hrat(dest_hrat a) = a) /\
    (!r. (\c. ?x. c = $trat_eq x)r = (dest_hrat(mk_hrat r) = r))
@@ -68,16 +65,16 @@
 \THEOREM trat\_1 HRAT
 |- trat_1 = 0,0
 \ENDTHEOREM
+\THEOREM TRAT\_ADD\_ASSOC HRAT
+|- !h i j.
+    (h trat_add (i trat_add j)) trat_eq ((h trat_add i) trat_add j)
+\ENDTHEOREM
 \THEOREM trat\_add HRAT
 |- !x y x' y'.
     (x,y) trat_add (x',y') =
     PRE(((SUC x) * (SUC y')) + ((SUC x') * (SUC y))),
     PRE((SUC y) * (SUC y'))
 \ENDTHEOREM
-\THEOREM TRAT\_ADD\_ASSOC HRAT
-|- !h i j.
-    (h trat_add (i trat_add j)) trat_eq ((h trat_add i) trat_add j)
-\ENDTHEOREM
 \THEOREM TRAT\_ADD\_SYM HRAT
 |- !h i. (h trat_add i) trat_eq (i trat_add h)
 \ENDTHEOREM
@@ -90,24 +87,24 @@
     (?d. h trat_eq (i trat_add d)) \/
     (?d. i trat_eq (h trat_add d))
 \ENDTHEOREM
-\THEOREM TRAT\_ADD\_WELLDEFINED HRAT
-|- !p q r. p trat_eq q ==> (p trat_add r) trat_eq (q trat_add r)
-\ENDTHEOREM
 \THEOREM TRAT\_ADD\_WELLDEFINED2 HRAT
 |- !p1 p2 q1 q2.
     p1 trat_eq p2 /\ q1 trat_eq q2 ==>
     (p1 trat_add q1) trat_eq (p2 trat_add q2)
 \ENDTHEOREM
+\THEOREM TRAT\_ADD\_WELLDEFINED HRAT
+|- !p q r. p trat_eq q ==> (p trat_add r) trat_eq (q trat_add r)
+\ENDTHEOREM
 \THEOREM TRAT\_ARCH HRAT
 |- !h. ?n d. (trat_sucint n) trat_eq (h trat_add d)
 \ENDTHEOREM
+\THEOREM TRAT\_EQ\_AP HRAT
+|- !p q. (p = q) ==> p trat_eq q
+\ENDTHEOREM
 \THEOREM trat\_eq HRAT
 |- !x y x' y'.
     (x,y) trat_eq (x',y') = ((SUC x) * (SUC y') = (SUC x') * (SUC y))
 \ENDTHEOREM
-\THEOREM TRAT\_EQ\_AP HRAT
-|- !p q. (p = q) ==> p trat_eq q
-\ENDTHEOREM
 \THEOREM TRAT\_EQ\_EQUIV HRAT
 |- !p q. p trat_eq q = ($trat_eq p = $trat_eq q)
 \ENDTHEOREM
@@ -131,15 +128,15 @@
     (h trat_mul (i trat_add j)) trat_eq
     ((h trat_mul i) trat_add (h trat_mul j))
 \ENDTHEOREM
+\THEOREM TRAT\_MUL\_ASSOC HRAT
+|- !h i j.
+    (h trat_mul (i trat_mul j)) trat_eq ((h trat_mul i) trat_mul j)
+\ENDTHEOREM
 \THEOREM trat\_mul HRAT
 |- !x y x' y'.
     (x,y) trat_mul (x',y') =
     PRE((SUC x) * (SUC x')),PRE((SUC y) * (SUC y'))
 \ENDTHEOREM
-\THEOREM TRAT\_MUL\_ASSOC HRAT
-|- !h i j.
-    (h trat_mul (i trat_mul j)) trat_eq ((h trat_mul i) trat_mul j)
-\ENDTHEOREM
 \THEOREM TRAT\_MUL\_LID HRAT
 |- !h. (trat_1 trat_mul h) trat_eq h
 \ENDTHEOREM
@@ -152,30 +149,29 @@
 \THEOREM TRAT\_MUL\_SYM\_EQ HRAT
 |- !h i. h trat_mul i = i trat_mul h
 \ENDTHEOREM
-\THEOREM TRAT\_MUL\_WELLDEFINED HRAT
-|- !p q r. p trat_eq q ==> (p trat_mul r) trat_eq (q trat_mul r)
-\ENDTHEOREM
 \THEOREM TRAT\_MUL\_WELLDEFINED2 HRAT
 |- !p1 p2 q1 q2.
     p1 trat_eq p2 /\ q1 trat_eq q2 ==>
     (p1 trat_mul q1) trat_eq (p2 trat_mul q2)
 \ENDTHEOREM
+\THEOREM TRAT\_MUL\_WELLDEFINED HRAT
+|- !p q r. p trat_eq q ==> (p trat_mul r) trat_eq (q trat_mul r)
+\ENDTHEOREM
 \THEOREM TRAT\_NOZERO HRAT
 |- !h i. ~(h trat_add i) trat_eq h
 \ENDTHEOREM
-\THEOREM TRAT\_SUCINT HRAT
-|- (trat_sucint 0) trat_eq trat_1 /\
-   (!n. (trat_sucint(SUC n)) trat_eq ((trat_sucint n) trat_add trat_1))
+\THEOREM TRAT\_SUCINT\_0 HRAT
+|- !n. (trat_sucint n) trat_eq (n,0)
 \ENDTHEOREM
 \THEOREM trat\_sucint HRAT
 |- (trat_sucint 0 = trat_1) /\
    (!n. trat_sucint(SUC n) = (trat_sucint n) trat_add trat_1)
 \ENDTHEOREM
-\THEOREM TRAT\_SUCINT\_0 HRAT
-|- !n. (trat_sucint n) trat_eq (n,0)
+\THEOREM TRAT\_SUCINT HRAT
+|- (trat_sucint 0) trat_eq trat_1 /\
+   (!n. (trat_sucint(SUC n)) trat_eq ((trat_sucint n) trat_add trat_1))
 \ENDTHEOREM
-\section{HREAL}
-\THEOREM CUT\_BOUNDED HREAL
+\section{HREAL}\THEOREM CUT\_BOUNDED HREAL
 |- !X. ?x. ~cut X x
 \ENDTHEOREM
 \THEOREM CUT\_DOWN HREAL
@@ -208,12 +204,12 @@
 \THEOREM EQUAL\_CUTS HREAL
 |- !X Y. (cut X = cut Y) ==> (X = Y)
 \ENDTHEOREM
-\THEOREM HRAT\_DOWN HREAL
-|- !x. ?y. y hrat_lt x
-\ENDTHEOREM
 \THEOREM HRAT\_DOWN2 HREAL
 |- !x y. ?z. z hrat_lt x /\ z hrat_lt y
 \ENDTHEOREM
+\THEOREM HRAT\_DOWN HREAL
+|- !x. ?y. y hrat_lt x
+\ENDTHEOREM
 \THEOREM HRAT\_EQ\_LADD HREAL
 |- !x y z. (x hrat_add y = x hrat_add z) = (y = z)
 \ENDTHEOREM
@@ -229,9 +225,6 @@
 \THEOREM HRAT\_INV\_MUL HREAL
 |- !x y. hrat_inv(x hrat_mul y) = (hrat_inv x) hrat_mul (hrat_inv y)
 \ENDTHEOREM
-\THEOREM hrat\_lt HREAL
-|- !x y. x hrat_lt y = (?d. y = x hrat_add d)
-\ENDTHEOREM
 \THEOREM HRAT\_LT\_ADD2 HREAL
 |- !u v x y.
     u hrat_lt x /\ v hrat_lt y ==> (u hrat_add v) hrat_lt (x hrat_add y)
@@ -245,6 +238,9 @@
 \THEOREM HRAT\_LT\_ANTISYM HREAL
 |- !x y. ~(x hrat_lt y /\ y hrat_lt x)
 \ENDTHEOREM
+\THEOREM hrat\_lt HREAL
+|- !x y. x hrat_lt y = (?d. y = x hrat_add d)
+\ENDTHEOREM
 \THEOREM HRAT\_LT\_GT HREAL
 |- !x y. x hrat_lt y ==> ~y hrat_lt x
 \ENDTHEOREM
@@ -254,12 +250,12 @@
 \THEOREM HRAT\_LT\_LADD HREAL
 |- !x y z. (z hrat_add x) hrat_lt (z hrat_add y) = x hrat_lt y
 \ENDTHEOREM
-\THEOREM HRAT\_LT\_LMUL HREAL
-|- !x y z. (z hrat_mul x) hrat_lt (z hrat_mul y) = x hrat_lt y
-\ENDTHEOREM
 \THEOREM HRAT\_LT\_LMUL1 HREAL
 |- !x y. (x hrat_mul y) hrat_lt y = x hrat_lt hrat_1
 \ENDTHEOREM
+\THEOREM HRAT\_LT\_LMUL HREAL
+|- !x y z. (z hrat_mul x) hrat_lt (z hrat_mul y) = x hrat_lt y
+\ENDTHEOREM
 \THEOREM HRAT\_LT\_MUL2 HREAL
 |- !u v x y.
     u hrat_lt x /\ v hrat_lt y ==> (u hrat_mul v) hrat_lt (x hrat_mul y)
@@ -276,12 +272,12 @@
 \THEOREM HRAT\_LT\_REFL HREAL
 |- !x. ~x hrat_lt x
 \ENDTHEOREM
-\THEOREM HRAT\_LT\_RMUL HREAL
-|- !x y z. (x hrat_mul z) hrat_lt (y hrat_mul z) = x hrat_lt y
-\ENDTHEOREM
 \THEOREM HRAT\_LT\_RMUL1 HREAL
 |- !x y. (x hrat_mul y) hrat_lt x = y hrat_lt hrat_1
 \ENDTHEOREM
+\THEOREM HRAT\_LT\_RMUL HREAL
+|- !x y z. (x hrat_mul z) hrat_lt (y hrat_mul z) = x hrat_lt y
+\ENDTHEOREM
 \THEOREM HRAT\_LT\_TOTAL HREAL
 |- !x y. (x = y) \/ x hrat_lt y \/ y hrat_lt x
 \ENDTHEOREM
@@ -307,14 +303,14 @@
 \THEOREM hreal\_1 HREAL
 |- hreal_1 = hreal(cut_of_hrat hrat_1)
 \ENDTHEOREM
+\THEOREM HREAL\_ADD\_ASSOC HREAL
+|- !X Y Z. X hreal_add (Y hreal_add Z) = (X hreal_add Y) hreal_add Z
+\ENDTHEOREM
 \THEOREM hreal\_add HREAL
 |- !X Y.
     X hreal_add Y =
     hreal(\w. ?x y. (w = x hrat_add y) /\ cut X x /\ cut Y y)
 \ENDTHEOREM
-\THEOREM HREAL\_ADD\_ASSOC HREAL
-|- !X Y Z. X hreal_add (Y hreal_add Z) = (X hreal_add Y) hreal_add Z
-\ENDTHEOREM
 \THEOREM HREAL\_ADD\_ISACUT HREAL
 |- !X Y. isacut(\w. ?x y. (w = x hrat_add y) /\ cut X x /\ cut Y y)
 \ENDTHEOREM
@@ -342,26 +338,26 @@
     X hreal_mul (Y hreal_add Z) =
     (X hreal_mul Y) hreal_add (X hreal_mul Z)
 \ENDTHEOREM
-\THEOREM HREAL\_LT HREAL
-|- !X Y. X hreal_lt Y = (?D. Y = X hreal_add D)
-\ENDTHEOREM
 \THEOREM hreal\_lt HREAL
 |- !X Y. X hreal_lt Y = ~(X = Y) /\ (!x. cut X x ==> cut Y x)
 \ENDTHEOREM
+\THEOREM HREAL\_LT HREAL
+|- !X Y. X hreal_lt Y = (?D. Y = X hreal_add D)
+\ENDTHEOREM
 \THEOREM HREAL\_LT\_LEMMA HREAL
 |- !X Y. X hreal_lt Y ==> (?x. ~cut X x /\ cut Y x)
 \ENDTHEOREM
 \THEOREM HREAL\_LT\_TOTAL HREAL
 |- !X Y. (X = Y) \/ X hreal_lt Y \/ Y hreal_lt X
 \ENDTHEOREM
+\THEOREM HREAL\_MUL\_ASSOC HREAL
+|- !X Y Z. X hreal_mul (Y hreal_mul Z) = (X hreal_mul Y) hreal_mul Z
+\ENDTHEOREM
 \THEOREM hreal\_mul HREAL
 |- !X Y.
     X hreal_mul Y =
     hreal(\w. ?x y. (w = x hrat_mul y) /\ cut X x /\ cut Y y)
 \ENDTHEOREM
-\THEOREM HREAL\_MUL\_ASSOC HREAL
-|- !X Y Z. X hreal_mul (Y hreal_mul Z) = (X hreal_mul Y) hreal_mul Z
-\ENDTHEOREM
 \THEOREM HREAL\_MUL\_ISACUT HREAL
 |- !X Y. isacut(\w. ?x y. (w = x hrat_mul y) /\ cut X x /\ cut Y y)
 \ENDTHEOREM
@@ -377,24 +373,24 @@
 \THEOREM HREAL\_NOZERO HREAL
 |- !X Y. ~(X hreal_add Y = X)
 \ENDTHEOREM
-\THEOREM hreal\_sub HREAL
-|- !Y X. Y hreal_sub X = hreal(\w. ?x. ~cut X x /\ cut Y(x hrat_add w))
-\ENDTHEOREM
 \THEOREM HREAL\_SUB\_ADD HREAL
 |- !X Y. X hreal_lt Y ==> ((Y hreal_sub X) hreal_add X = Y)
 \ENDTHEOREM
+\THEOREM hreal\_sub HREAL
+|- !Y X. Y hreal_sub X = hreal(\w. ?x. ~cut X x /\ cut Y(x hrat_add w))
+\ENDTHEOREM
 \THEOREM HREAL\_SUB\_ISACUT HREAL
 |- !X Y.
     X hreal_lt Y ==> isacut(\w. ?x. ~cut X x /\ cut Y(x hrat_add w))
 \ENDTHEOREM
+\THEOREM hreal\_sup HREAL
+|- !P. hreal_sup P = hreal(\w. ?X. P X /\ cut X w)
+\ENDTHEOREM
 \THEOREM HREAL\_SUP HREAL
 |- !P.
     (?X. P X) /\ (?Y. !X. P X ==> X hreal_lt Y) ==>
     (!Y. (?X. P X /\ Y hreal_lt X) = Y hreal_lt (hreal_sup P))
 \ENDTHEOREM
-\THEOREM hreal\_sup HREAL
-|- !P. hreal_sup P = hreal(\w. ?X. P X /\ cut X w)
-\ENDTHEOREM
 \THEOREM HREAL\_SUP\_ISACUT HREAL
 |- !P.
     (?X. P X) /\ (?Y. !X. P X ==> X hreal_lt Y) ==>
@@ -417,8 +413,7 @@
 \THEOREM ISACUT\_HRAT HREAL
 |- !h. isacut(cut_of_hrat h)
 \ENDTHEOREM
-\section{REALAX}
-\THEOREM HREAL\_EQ\_ADDL REALAX
+\section{REALAX}\THEOREM HREAL\_EQ\_ADDL REALAX
 |- !x y. ~(x = x hreal_add y)
 \ENDTHEOREM
 \THEOREM HREAL\_EQ\_ADDR REALAX
@@ -470,15 +465,15 @@
 \THEOREM REAL\_10 REALAX
 |- ~(r1 = r0)
 \ENDTHEOREM
+\THEOREM REAL\_ADD\_ASSOC REALAX
+|- !x y z. x + (y + z) = (x + y) + z
+\ENDTHEOREM
 \THEOREM real\_add REALAX
 |- !g00025 g00026.
     g00025 + g00026 =
     mk_real
     ($treal_eq(($@(dest_real g00025)) treal_add ($@(dest_real g00026))))
 \ENDTHEOREM
-\THEOREM REAL\_ADD\_ASSOC REALAX
-|- !x y z. x + (y + z) = (x + y) + z
-\ENDTHEOREM
 \THEOREM REAL\_ADD\_LID REALAX
 |- !x. r0 + x = x
 \ENDTHEOREM
@@ -518,15 +513,15 @@
 \THEOREM REAL\_LT\_TRANS REALAX
 |- !x y z. x < y /\ y < z ==> x < z
 \ENDTHEOREM
+\THEOREM REAL\_MUL\_ASSOC REALAX
+|- !x y z. x * (y * z) = (x * y) * z
+\ENDTHEOREM
 \THEOREM real\_mul REALAX
 |- !g00027 g00028.
     g00027 * g00028 =
     mk_real
     ($treal_eq(($@(dest_real g00027)) treal_mul ($@(dest_real g00028))))
 \ENDTHEOREM
-\THEOREM REAL\_MUL\_ASSOC REALAX
-|- !x y z. x * (y * z) = (x * y) * z
-\ENDTHEOREM
 \THEOREM REAL\_MUL\_LID REALAX
 |- !x. r1 * x = x
 \ENDTHEOREM
@@ -578,19 +573,19 @@
 \THEOREM treal\_0 REALAX
 |- treal_0 = hreal_1,hreal_1
 \ENDTHEOREM
+\THEOREM TREAL\_10 REALAX
+|- ~treal_1 treal_eq treal_0
+\ENDTHEOREM
 \THEOREM treal\_1 REALAX
 |- treal_1 = hreal_1 hreal_add hreal_1,hreal_1
 \ENDTHEOREM
-\THEOREM TREAL\_10 REALAX
-|- ~treal_1 treal_eq treal_0
+\THEOREM TREAL\_ADD\_ASSOC REALAX
+|- !x y z. x treal_add (y treal_add z) = (x treal_add y) treal_add z
 \ENDTHEOREM
 \THEOREM treal\_add REALAX
 |- !x1 y1 x2 y2.
     (x1,y1) treal_add (x2,y2) = x1 hreal_add x2,y1 hreal_add y2
 \ENDTHEOREM
-\THEOREM TREAL\_ADD\_ASSOC REALAX
-|- !x y z. x treal_add (y treal_add z) = (x treal_add y) treal_add z
-\ENDTHEOREM
 \THEOREM TREAL\_ADD\_LID REALAX
 |- !x. (treal_0 treal_add x) treal_eq x
 \ENDTHEOREM
@@ -617,13 +612,13 @@
 \THEOREM TREAL\_BIJ\_WELLDEF REALAX
 |- !h i. h treal_eq i ==> (hreal_of_treal h = hreal_of_treal i)
 \ENDTHEOREM
+\THEOREM TREAL\_EQ\_AP REALAX
+|- !p q. (p = q) ==> p treal_eq q
+\ENDTHEOREM
 \THEOREM treal\_eq REALAX
 |- !x1 y1 x2 y2.
     (x1,y1) treal_eq (x2,y2) = (x1 hreal_add y2 = x2 hreal_add y1)
 \ENDTHEOREM
-\THEOREM TREAL\_EQ\_AP REALAX
-|- !p q. (p = q) ==> p treal_eq q
-\ENDTHEOREM
 \THEOREM TREAL\_EQ\_EQUIV REALAX
 |- !p q. p treal_eq q = ($treal_eq p = $treal_eq q)
 \ENDTHEOREM
@@ -656,14 +651,14 @@
     x treal_mul (y treal_add z) =
     (x treal_mul y) treal_add (x treal_mul z)
 \ENDTHEOREM
+\THEOREM TREAL\_LT\_ADD REALAX
+|- !x y z. y treal_lt z ==> (x treal_add y) treal_lt (x treal_add z)
+\ENDTHEOREM
 \THEOREM treal\_lt REALAX
 |- !x1 y1 x2 y2.
     (x1,y1) treal_lt (x2,y2) =
     (x1 hreal_add y2) hreal_lt (x2 hreal_add y1)
 \ENDTHEOREM
-\THEOREM TREAL\_LT\_ADD REALAX
-|- !x y z. y treal_lt z ==> (x treal_add y) treal_lt (x treal_add z)
-\ENDTHEOREM
 \THEOREM TREAL\_LT\_MUL REALAX
 |- !x y.
     treal_0 treal_lt x /\ treal_0 treal_lt y ==>
@@ -689,15 +684,15 @@
 \THEOREM TREAL\_LT\_WELLDEFR REALAX
 |- !x1 x2 y. x1 treal_eq x2 ==> (x1 treal_lt y = x2 treal_lt y)
 \ENDTHEOREM
+\THEOREM TREAL\_MUL\_ASSOC REALAX
+|- !x y z. x treal_mul (y treal_mul z) = (x treal_mul y) treal_mul z
+\ENDTHEOREM
 \THEOREM treal\_mul REALAX
 |- !x1 y1 x2 y2.
     (x1,y1) treal_mul (x2,y2) =
     (x1 hreal_mul x2) hreal_add (y1 hreal_mul y2),
     (x1 hreal_mul y2) hreal_add (y1 hreal_mul x2)
 \ENDTHEOREM
-\THEOREM TREAL\_MUL\_ASSOC REALAX
-|- !x y z. x treal_mul (y treal_mul z) = (x treal_mul y) treal_mul z
-\ENDTHEOREM
 \THEOREM TREAL\_MUL\_LID REALAX
 |- !x. (treal_1 treal_mul x) treal_eq x
 \ENDTHEOREM
@@ -726,11 +721,7 @@
 \THEOREM treal\_of\_hreal REALAX
 |- !x. treal_of_hreal x = x hreal_add hreal_1,hreal_1
 \ENDTHEOREM
-\section{REAL}
-\THEOREM abs REAL
-|- !x. abs x = ((& 0) <= x => x | -- x)
-\ENDTHEOREM
-\THEOREM REAL\_ABS\_0 REAL
+\section{REAL}\THEOREM REAL\_ABS\_0 REAL
 |- abs(& 0) = & 0
 \ENDTHEOREM
 \THEOREM REAL\_ABS\_1 REAL
@@ -739,9 +730,6 @@
 \THEOREM REAL\_ABS\_ABS REAL
 |- !x. abs(abs x) = abs x
 \ENDTHEOREM
-\THEOREM REAL\_ABS\_BETWEEN REAL
-|- !x y d. (& 0) < d /\ (x - d) < y /\ y < (x + d) = (abs(y - x)) < d
-\ENDTHEOREM
 \THEOREM REAL\_ABS\_BETWEEN1 REAL
 |- !x y z. x < z /\ (abs(y - x)) < (z - x) ==> y < z
 \ENDTHEOREM
@@ -752,6 +740,9 @@
     (abs(y - y0)) < ((y0 - x0) / (& 2)) ==>
     x < y
 \ENDTHEOREM
+\THEOREM REAL\_ABS\_BETWEEN REAL
+|- !x y d. (& 0) < d /\ (x - d) < y /\ y < (x + d) = (abs(y - x)) < d
+\ENDTHEOREM
 \THEOREM REAL\_ABS\_BOUND REAL
 |- !x y d. (abs(x - y)) < d ==> y < (x + d)
 \ENDTHEOREM
@@ -767,6 +758,9 @@
 \THEOREM REAL\_ABS\_DIV REAL
 |- !y. ~(y = & 0) ==> (!x. abs(x / y) = (abs x) / (abs y))
 \ENDTHEOREM
+\THEOREM abs REAL
+|- !x. abs x = ((& 0) <= x => x | -- x)
+\ENDTHEOREM
 \THEOREM REAL\_ABS\_INV REAL
 |- !x. ~(x = & 0) ==> (abs(inv x) = inv(abs x))
 \ENDTHEOREM
@@ -797,21 +791,21 @@
 \THEOREM REAL\_ABS\_REFL REAL
 |- !x. (abs x = x) = (& 0) <= x
 \ENDTHEOREM
-\THEOREM REAL\_ABS\_SIGN REAL
-|- !x y. (abs(x - y)) < y ==> (& 0) < x
-\ENDTHEOREM
 \THEOREM REAL\_ABS\_SIGN2 REAL
 |- !x y. (abs(x - y)) < (-- y) ==> x < (& 0)
 \ENDTHEOREM
+\THEOREM REAL\_ABS\_SIGN REAL
+|- !x y. (abs(x - y)) < y ==> (& 0) < x
+\ENDTHEOREM
 \THEOREM REAL\_ABS\_STILLNZ REAL
 |- !x y. (abs(x - y)) < (abs y) ==> ~(x = & 0)
 \ENDTHEOREM
-\THEOREM REAL\_ABS\_SUB REAL
-|- !x y. abs(x - y) = abs(y - x)
-\ENDTHEOREM
 \THEOREM REAL\_ABS\_SUB\_ABS REAL
 |- !x y. (abs((abs x) - (abs y))) <= (abs(x - y))
 \ENDTHEOREM
+\THEOREM REAL\_ABS\_SUB REAL
+|- !x y. abs(x - y) = abs(y - x)
+\ENDTHEOREM
 \THEOREM ABS\_SUM REAL
 |- !f m n. (abs(Sum(m,n)f)) <= (Sum(m,n)(\n'. abs(f n')))
 \ENDTHEOREM
@@ -821,9 +815,6 @@
 \THEOREM REAL\_ABS\_ZERO REAL
 |- !x. (abs x = & 0) = (x = & 0)
 \ENDTHEOREM
-\THEOREM pow REAL
-|- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
-\ENDTHEOREM
 \THEOREM POW\_0 REAL
 |- !n. (& 0) pow (SUC n) = & 0
 \ENDTHEOREM
@@ -845,6 +836,9 @@
 \THEOREM POW\_ADD REAL
 |- !c m n. c pow (m num_add n) = (c pow m) * (c pow n)
 \ENDTHEOREM
+\THEOREM pow REAL
+|- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
+\ENDTHEOREM
 \THEOREM POW\_INV REAL
 |- !c. ~(c = & 0) ==> (!n. inv(c pow n) = (inv c) pow n)
 \ENDTHEOREM
@@ -872,20 +866,14 @@
 \THEOREM POW\_POS\_LT REAL
 |- !x n. (& 0) < x ==> (& 0) < (x pow (SUC n))
 \ENDTHEOREM
-\THEOREM REAL REAL
-|- !n. &(SUC n) = (& n) + (& 1)
-\ENDTHEOREM
 \THEOREM REAL\_0 REAL
 |- r0 = & 0
 \ENDTHEOREM
-\THEOREM REAL\_1 REAL
-|- r1 = & 1
-\ENDTHEOREM
 \THEOREM REAL\_10 REAL
 |- ~(& 1 = & 0)
 \ENDTHEOREM
-\THEOREM REAL\_ADD REAL
-|- !m n. (& m) + (& n) = &(m num_add n)
+\THEOREM REAL\_1 REAL
+|- r1 = & 1
 \ENDTHEOREM
 \THEOREM REAL\_ADD2\_SUB2 REAL
 |- !a b c d. (a + b) - (c + d) = (a - c) + (b - d)
@@ -893,6 +881,9 @@
 \THEOREM REAL\_ADD\_ASSOC REAL
 |- !x y z. x + (y + z) = (x + y) + z
 \ENDTHEOREM
+\THEOREM REAL\_ADD REAL
+|- !m n. (& m) + (& n) = &(m num_add n)
+\ENDTHEOREM
 \THEOREM REAL\_ADD\_LID REAL
 |- !x. (& 0) + x = x
 \ENDTHEOREM
@@ -911,12 +902,12 @@
 \THEOREM REAL\_ADD\_RINV REAL
 |- !x. x + (-- x) = & 0
 \ENDTHEOREM
-\THEOREM REAL\_ADD\_SUB REAL
-|- !x y. (x + y) - x = y
-\ENDTHEOREM
 \THEOREM REAL\_ADD\_SUB2 REAL
 |- !x y. x - (x + y) = -- y
 \ENDTHEOREM
+\THEOREM REAL\_ADD\_SUB REAL
+|- !x y. (x + y) - x = y
+\ENDTHEOREM
 \THEOREM REAL\_ADD\_SYM REAL
 |- !x y. x + y = y + x
 \ENDTHEOREM
@@ -949,15 +940,18 @@
 \THEOREM REAL\_DIV\_RMUL REAL
 |- !x y. ~(y = & 0) ==> ((x / y) * y = x)
 \ENDTHEOREM
+\THEOREM REAL REAL
+|- !n. &(SUC n) = (& n) + (& 1)
+\ENDTHEOREM
 \THEOREM REAL\_DOUBLE REAL
 |- !x. x + x = (& 2) * x
 \ENDTHEOREM
-\THEOREM REAL\_DOWN REAL
-|- !x. (& 0) < x ==> (?y. (& 0) < y /\ y < x)
-\ENDTHEOREM
 \THEOREM REAL\_DOWN2 REAL
 |- !x y. (& 0) < x /\ (& 0) < y ==> (?z. (& 0) < z /\ z < x /\ z < y)
 \ENDTHEOREM
+\THEOREM REAL\_DOWN REAL
+|- !x. (& 0) < x ==> (?y. (& 0) < y /\ y < x)
+\ENDTHEOREM
 \THEOREM REAL\_ENTIRE REAL
 |- !x y. (x * y = & 0) = (x = & 0) \/ (y = & 0)
 \ENDTHEOREM
@@ -967,12 +961,12 @@
 \THEOREM REAL\_EQ\_LADD REAL
 |- !x y z. (x + y = x + z) = (y = z)
 \ENDTHEOREM
-\THEOREM REAL\_EQ\_LMUL REAL
-|- !x y z. (x * y = x * z) = (x = & 0) \/ (y = z)
-\ENDTHEOREM
 \THEOREM REAL\_EQ\_LMUL2 REAL
 |- !x y z. ~(x = & 0) ==> ((y = z) = (x * y = x * z))
 \ENDTHEOREM
+\THEOREM REAL\_EQ\_LMUL REAL
+|- !x y z. (x * y = x * z) = (x = & 0) \/ (y = z)
+\ENDTHEOREM
 \THEOREM REAL\_EQ\_LMUL\_IMP REAL
 |- !x y z. ~(x = & 0) /\ (x * y = x * z) ==> (y = z)
 \ENDTHEOREM
@@ -1012,12 +1006,12 @@
 \THEOREM REAL\_INV1 REAL
 |- inv(& 1) = & 1
 \ENDTHEOREM
-\THEOREM REAL\_INVINV REAL
-|- !x. ~(x = & 0) ==> (inv(inv x) = x)
-\ENDTHEOREM
 \THEOREM REAL\_INV\_1OVER REAL
 |- !x. inv x = (& 1) / x
 \ENDTHEOREM
+\THEOREM REAL\_INVINV REAL
+|- !x. ~(x = & 0) ==> (inv(inv x) = x)
+\ENDTHEOREM
 \THEOREM REAL\_INV\_LT1 REAL
 |- !x. (& 0) < x /\ x < (& 1) ==> (& 1) < (inv x)
 \ENDTHEOREM
@@ -1033,39 +1027,18 @@
 \THEOREM REAL\_LDISTRIB REAL
 |- !x y z. x * (y + z) = (x * y) + (x * z)
 \ENDTHEOREM
-\THEOREM REAL\_LE REAL
-|- !m n. (& m) <= (& n) = m num_le n
-\ENDTHEOREM
-\THEOREM real\_le REAL
-|- !x y. x <= y = ~y < x
+\THEOREM REAL\_LE\_01 REAL
+|- (& 0) <= (& 1)
 \ENDTHEOREM
 \THEOREM REAL\_LE1\_POW2 REAL
 |- !x. (& 1) <= x ==> (& 1) <= (x pow 2)
 \ENDTHEOREM
-\THEOREM REAL\_LET\_ADD REAL
-|- !x y. (& 0) <= x /\ (& 0) < y ==> (& 0) < (x + y)
-\ENDTHEOREM
-\THEOREM REAL\_LET\_ADD2 REAL
-|- !w x y z. w <= x /\ y < z ==> (w + y) < (x + z)
-\ENDTHEOREM
-\THEOREM REAL\_LET\_ANTISYM REAL
-|- !x y. ~(x < y /\ y <= x)
-\ENDTHEOREM
-\THEOREM REAL\_LET\_TOTAL REAL
-|- !x y. x <= y \/ y < x
-\ENDTHEOREM
-\THEOREM REAL\_LET\_TRANS REAL
-|- !x y z. x <= y /\ y < z ==> x < z
-\ENDTHEOREM
-\THEOREM REAL\_LE\_01 REAL
-|- (& 0) <= (& 1)
+\THEOREM REAL\_LE\_ADD2 REAL
+|- !w x y z. w <= x /\ y <= z ==> (w + y) <= (x + z)
 \ENDTHEOREM
 \THEOREM REAL\_LE\_ADD REAL
 |- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x + y)
 \ENDTHEOREM
-\THEOREM REAL\_LE\_ADD2 REAL
-|- !w x y z. w <= x /\ y <= z ==> (w + y) <= (x + z)
-\ENDTHEOREM
 \THEOREM REAL\_LE\_ADDL REAL
 |- !x y. y <= (x + y) = (& 0) <= x
 \ENDTHEOREM
@@ -1075,7 +1048,13 @@
 \THEOREM REAL\_LE\_ANTISYM REAL
 |- !x y. x <= y /\ y <= x = (x = y)
 \ENDTHEOREM
-\THEOREM REAL\_LE\_DOUBLE REAL
+\THEOREM real\_le REAL
+|- !x y. x <= y = ~y < x
+\ENDTHEOREM
+\THEOREM REAL\_LE REAL
+|- !m n. (& m) <= (& n) = m num_le n
+\ENDTHEOREM
+\THEOREM REAL\_LE\_DOUBLE REAL
 |- !x. (& 0) <= (x + x) = (& 0) <= x
 \ENDTHEOREM
 \THEOREM REAL\_LE\_LADD REAL
@@ -1093,14 +1072,14 @@
 \THEOREM REAL\_LE\_LT REAL
 |- !x y. x <= y = x < y \/ (x = y)
 \ENDTHEOREM
-\THEOREM REAL\_LE\_MUL REAL
-|- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x * y)
-\ENDTHEOREM
 \THEOREM REAL\_LE\_MUL2 REAL
 |- !x1 x2 y1 y2.
     (& 0) <= x1 /\ (& 0) <= y1 /\ x1 <= x2 /\ y1 <= y2 ==>
     (x1 * y1) <= (x2 * y2)
 \ENDTHEOREM
+\THEOREM REAL\_LE\_MUL REAL
+|- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x * y)
+\ENDTHEOREM
 \THEOREM REAL\_LE\_NEG REAL
 |- !x y. (-- x) <= (-- y) = y <= x
 \ENDTHEOREM
@@ -1140,47 +1119,41 @@
 \THEOREM REAL\_LE\_SUB\_RADD REAL
 |- !x y z. (x - y) <= z = x <= (z + y)
 \ENDTHEOREM
+\THEOREM REAL\_LET\_ADD2 REAL
+|- !w x y z. w <= x /\ y < z ==> (w + y) < (x + z)
+\ENDTHEOREM
+\THEOREM REAL\_LET\_ADD REAL
+|- !x y. (& 0) <= x /\ (& 0) < y ==> (& 0) < (x + y)
+\ENDTHEOREM
+\THEOREM REAL\_LET\_ANTISYM REAL
+|- !x y. ~(x < y /\ y <= x)
+\ENDTHEOREM
 \THEOREM REAL\_LE\_TOTAL REAL
 |- !x y. x <= y \/ y <= x
 \ENDTHEOREM
 \THEOREM REAL\_LE\_TRANS REAL
 |- !x y z. x <= y /\ y <= z ==> x <= z
 \ENDTHEOREM
+\THEOREM REAL\_LET\_TOTAL REAL
+|- !x y. x <= y \/ y < x
+\ENDTHEOREM
+\THEOREM REAL\_LET\_TRANS REAL
+|- !x y z. x <= y /\ y < z ==> x < z
+\ENDTHEOREM
 \THEOREM REAL\_LINV\_UNIQ REAL
 |- !x y. (x * y = & 1) ==> (x = inv y)
 \ENDTHEOREM
 \THEOREM REAL\_LNEG\_UNIQ REAL
 |- !x y. (x + y = & 0) = (x = -- y)
 \ENDTHEOREM
-\THEOREM REAL\_LT REAL
-|- !m n. (& m) < (& n) = m num_lt n
-\ENDTHEOREM
-\THEOREM REAL\_LT1\_POW2 REAL
-|- !x. (& 1) < x ==> (& 1) < (x pow 2)
-\ENDTHEOREM
-\THEOREM REAL\_LTE\_ADD REAL
-|- !x y. (& 0) < x /\ (& 0) <= y ==> (& 0) < (x + y)
-\ENDTHEOREM
-\THEOREM REAL\_LTE\_ADD2 REAL
-|- !w x y z. w < x /\ y <= z ==> (w + y) < (x + z)
-\ENDTHEOREM
-\THEOREM REAL\_LTE\_ANTSYM REAL
-|- !x y. ~(x <= y /\ y < x)
-\ENDTHEOREM
-\THEOREM REAL\_LTE\_TOTAL REAL
-|- !x y. x < y \/ y <= x
-\ENDTHEOREM
-\THEOREM REAL\_LTE\_TRANS REAL
-|- !x y z. x < y /\ y <= z ==> x < z
-\ENDTHEOREM
 \THEOREM REAL\_LT\_01 REAL
 |- (& 0) < (& 1)
 \ENDTHEOREM
 \THEOREM REAL\_LT\_1 REAL
 |- !x y. (& 0) <= x /\ x < y ==> (x / y) < (& 1)
 \ENDTHEOREM
-\THEOREM REAL\_LT\_ADD REAL
-|- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x + y)
+\THEOREM REAL\_LT1\_POW2 REAL
+|- !x. (& 1) < x ==> (& 1) < (x pow 2)
 \ENDTHEOREM
 \THEOREM REAL\_LT\_ADD1 REAL
 |- !x y. x <= y ==> x < (y + (& 1))
@@ -1188,15 +1161,18 @@
 \THEOREM REAL\_LT\_ADD2 REAL
 |- !w x y z. w < x /\ y < z ==> (w + y) < (x + z)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_ADD REAL
+|- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x + y)
+\ENDTHEOREM
 \THEOREM REAL\_LT\_ADDL REAL
 |- !x y. y < (x + y) = (& 0) < x
 \ENDTHEOREM
-\THEOREM REAL\_LT\_ADDNEG REAL
-|- !x y z. y < (x + (-- z)) = (y + z) < x
-\ENDTHEOREM
 \THEOREM REAL\_LT\_ADDNEG2 REAL
 |- !x y z. (x + (-- y)) < z = x < (z + y)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_ADDNEG REAL
+|- !x y z. y < (x + (-- z)) = (y + z) < x
+\ENDTHEOREM
 \THEOREM REAL\_LT\_ADDR REAL
 |- !x y. x < (x + y) = (& 0) < y
 \ENDTHEOREM
@@ -1206,12 +1182,30 @@
 \THEOREM REAL\_LT\_ANTISYM REAL
 |- !x y. ~(x < y /\ y < x)
 \ENDTHEOREM
-\THEOREM REAL\_LT\_FRACTION REAL
-|- !n d. 1 num_lt n ==> ((d / (& n)) < d = (& 0) < d)
+\THEOREM REAL\_LT REAL
+|- !m n. (& m) < (& n) = m num_lt n
+\ENDTHEOREM
+\THEOREM REAL\_LTE\_ADD2 REAL
+|- !w x y z. w < x /\ y <= z ==> (w + y) < (x + z)
+\ENDTHEOREM
+\THEOREM REAL\_LTE\_ADD REAL
+|- !x y. (& 0) < x /\ (& 0) <= y ==> (& 0) < (x + y)
+\ENDTHEOREM
+\THEOREM REAL\_LTE\_ANTSYM REAL
+|- !x y. ~(x <= y /\ y < x)
+\ENDTHEOREM
+\THEOREM REAL\_LTE\_TOTAL REAL
+|- !x y. x < y \/ y <= x
+\ENDTHEOREM
+\THEOREM REAL\_LTE\_TRANS REAL
+|- !x y z. x < y /\ y <= z ==> x < z
 \ENDTHEOREM
 \THEOREM REAL\_LT\_FRACTION\_0 REAL
 |- !n d. ~(n = 0) ==> ((& 0) < (d / (& n)) = (& 0) < d)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_FRACTION REAL
+|- !n d. 1 num_lt n ==> ((d / (& n)) < d = (& 0) < d)
+\ENDTHEOREM
 \THEOREM REAL\_LT\_GT REAL
 |- !x y. x < y ==> ~y < x
 \ENDTHEOREM
@@ -1239,23 +1233,23 @@
 \THEOREM REAL\_LT\_LE REAL
 |- !x y. x < y = x <= y /\ ~(x = y)
 \ENDTHEOREM
-\THEOREM REAL\_LT\_LMUL REAL
-|- !x y z. (& 0) < x ==> ((x * y) < (x * z) = y < z)
-\ENDTHEOREM
 \THEOREM REAL\_LT\_LMUL\_0 REAL
 |- !x y. (& 0) < x ==> ((& 0) < (x * y) = (& 0) < y)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_LMUL REAL
+|- !x y z. (& 0) < x ==> ((x * y) < (x * z) = y < z)
+\ENDTHEOREM
 \THEOREM REAL\_LT\_LMUL\_IMP REAL
 |- !x y z. y < z /\ (& 0) < x ==> (x * y) < (x * z)
 \ENDTHEOREM
-\THEOREM REAL\_LT\_MUL REAL
-|- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x * y)
-\ENDTHEOREM
 \THEOREM REAL\_LT\_MUL2 REAL
 |- !x1 x2 y1 y2.
     (& 0) <= x1 /\ (& 0) <= y1 /\ x1 < x2 /\ y1 < y2 ==>
     (x1 * y1) < (x2 * y2)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_MUL REAL
+|- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x * y)
+\ENDTHEOREM
 \THEOREM REAL\_LT\_MULTIPLE REAL
 |- !n d. 1 num_lt n ==> (d < ((& n) * d) = (& 0) < d)
 \ENDTHEOREM
@@ -1271,21 +1265,21 @@
 \THEOREM REAL\_LT\_RADD REAL
 |- !x y z. (x + z) < (y + z) = x < y
 \ENDTHEOREM
-\THEOREM REAL\_LT\_RDIV REAL
-|- !x y z. (& 0) < z ==> ((x / z) < (y / z) = x < y)
-\ENDTHEOREM
 \THEOREM REAL\_LT\_RDIV\_0 REAL
 |- !y z. (& 0) < z ==> ((& 0) < (y / z) = (& 0) < y)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_RDIV REAL
+|- !x y z. (& 0) < z ==> ((x / z) < (y / z) = x < y)
+\ENDTHEOREM
 \THEOREM REAL\_LT\_REFL REAL
 |- !x. ~x < x
 \ENDTHEOREM
-\THEOREM REAL\_LT\_RMUL REAL
-|- !x y z. (& 0) < z ==> ((x * z) < (y * z) = x < y)
-\ENDTHEOREM
 \THEOREM REAL\_LT\_RMUL\_0 REAL
 |- !x y. (& 0) < y ==> ((& 0) < (x * y) = (& 0) < x)
 \ENDTHEOREM
+\THEOREM REAL\_LT\_RMUL REAL
+|- !x y z. (& 0) < z ==> ((x * z) < (y * z) = x < y)
+\ENDTHEOREM
 \THEOREM REAL\_LT\_RMUL\_IMP REAL
 |- !x y z. x < y /\ (& 0) < z ==> (x * z) < (y * z)
 \ENDTHEOREM
@@ -1304,12 +1298,12 @@
 \THEOREM REAL\_MEAN REAL
 |- !x y. x < y ==> (?z. x < z /\ z < y)
 \ENDTHEOREM
-\THEOREM REAL\_MUL REAL
-|- !m n. (& m) * (& n) = &(m num_mul n)
-\ENDTHEOREM
 \THEOREM REAL\_MUL\_ASSOC REAL
 |- !x y z. x * (y * z) = (x * y) * z
 \ENDTHEOREM
+\THEOREM REAL\_MUL REAL
+|- !m n. (& m) * (& n) = &(m num_mul n)
+\ENDTHEOREM
 \THEOREM REAL\_MUL\_LID REAL
 |- !x. (& 1) * x = x
 \ENDTHEOREM
@@ -1331,21 +1325,18 @@
 \THEOREM REAL\_MUL\_SYM REAL
 |- !x y. x * y = y * x
 \ENDTHEOREM
-\THEOREM REAL\_NEGNEG REAL
-|- !x. --(-- x) = x
-\ENDTHEOREM
 \THEOREM REAL\_NEG\_0 REAL
 |- --(& 0) = & 0
 \ENDTHEOREM
 \THEOREM REAL\_NEG\_ADD REAL
 |- !x y. --(x + y) = (-- x) + (-- y)
 \ENDTHEOREM
-\THEOREM REAL\_NEG\_EQ REAL
-|- !x y. (-- x = y) = (x = -- y)
-\ENDTHEOREM
 \THEOREM REAL\_NEG\_EQ0 REAL
 |- !x. (-- x = & 0) = (x = & 0)
 \ENDTHEOREM
+\THEOREM REAL\_NEG\_EQ REAL
+|- !x y. (-- x = y) = (x = -- y)
+\ENDTHEOREM
 \THEOREM REAL\_NEG\_GE0 REAL
 |- !x. (& 0) <= (-- x) = x <= (& 0)
 \ENDTHEOREM
@@ -1370,6 +1361,9 @@
 \THEOREM REAL\_NEG\_MUL2 REAL
 |- !x y. (-- x) * (-- y) = x * y
 \ENDTHEOREM
+\THEOREM REAL\_NEGNEG REAL
+|- !x. --(-- x) = x
+\ENDTHEOREM
 \THEOREM REAL\_NEG\_RMUL REAL
 |- !x y. --(x * y) = x * (-- y)
 \ENDTHEOREM
@@ -1412,20 +1406,20 @@
 \THEOREM REAL\_RNEG\_UNIQ REAL
 |- !x y. (x + y = & 0) = (y = -- x)
 \ENDTHEOREM
-\THEOREM real\_sub REAL
-|- !x y. x - y = x + (-- y)
-\ENDTHEOREM
 \THEOREM REAL\_SUB\_0 REAL
 |- !x y. (x - y = & 0) = (x = y)
 \ENDTHEOREM
 \THEOREM REAL\_SUB\_ABS REAL
 |- !x y. ((abs x) - (abs y)) <= (abs(x - y))
 \ENDTHEOREM
+\THEOREM REAL\_SUB\_ADD2 REAL
+|- !x y. y + (x - y) = x
+\ENDTHEOREM
 \THEOREM REAL\_SUB\_ADD REAL
 |- !x y. (x - y) + y = x
 \ENDTHEOREM
-\THEOREM REAL\_SUB\_ADD2 REAL
-|- !x y. y + (x - y) = x
+\THEOREM real\_sub REAL
+|- !x y. x - y = x + (-- y)
 \ENDTHEOREM
 \THEOREM REAL\_SUB\_INV2 REAL
 |- !x y.
@@ -1461,28 +1455,28 @@
 \THEOREM REAL\_SUB\_RZERO REAL
 |- !x. x - (& 0) = x
 \ENDTHEOREM
-\THEOREM REAL\_SUB\_SUB REAL
-|- !x y. (x - y) - x = -- y
-\ENDTHEOREM
 \THEOREM REAL\_SUB\_SUB2 REAL
 |- !x y. x - (x - y) = y
 \ENDTHEOREM
+\THEOREM REAL\_SUB\_SUB REAL
+|- !x y. (x - y) - x = -- y
+\ENDTHEOREM
 \THEOREM REAL\_SUB\_TRIANGLE REAL
 |- !a b c. (a - b) + (b - c) = a - c
 \ENDTHEOREM
 \THEOREM REAL\_SUMSQ REAL
 |- !x y. ((x * x) + (y * y) = & 0) = (x = & 0) /\ (y = & 0)
 \ENDTHEOREM
-\THEOREM REAL\_SUP REAL
-|- !P.
-    (?x. P x) /\ (?z. !x. P x ==> x < z) ==>
-    (!y. (?x. P x /\ y < x) = y < (sup P))
-\ENDTHEOREM
 \THEOREM REAL\_SUP\_ALLPOS REAL
 |- !P.
     (!x. P x ==> (& 0) < x) /\ (?x. P x) /\ (?z. !x. P x ==> x < z) ==>
     (?s. !y. (?x. P x /\ y < x) = y < s)
 \ENDTHEOREM
+\THEOREM REAL\_SUP REAL
+|- !P.
+    (?x. P x) /\ (?z. !x. P x ==> x < z) ==>
+    (!y. (?x. P x /\ y < x) = y < (sup P))
+\ENDTHEOREM
 \THEOREM REAL\_SUP\_EXISTS REAL
 |- !P.
     (?x. P x) /\ (?z. !x. P x ==> x < z) ==>
@@ -1511,13 +1505,6 @@
     (?x. P x) /\ (?z. !x. P x ==> x <= z) =
     (?x. P x) /\ (?z. !x. P x ==> x < z)
 \ENDTHEOREM
-\THEOREM Sum REAL
-|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
-\ENDTHEOREM
-\THEOREM sum REAL
-|- (!n f. sum n 0 f = & 0) /\
-   (!n m f. sum n(SUC m)f = (sum n m f) + (f(n num_add m)))
-\ENDTHEOREM
 \THEOREM SUM\_0 REAL
 |- !m n. Sum(m,n)(\r. & 0) = & 0
 \ENDTHEOREM
@@ -1550,6 +1537,13 @@
 \THEOREM SUM\_DIFF REAL
 |- !f m n. Sum(m,n)f = (Sum(0,m num_add n)f) - (Sum(0,m)f)
 \ENDTHEOREM
+\THEOREM sum REAL
+|- (!n f. sum n 0 f = & 0) /\
+   (!n m f. sum n(SUC m)f = (sum n m f) + (f(n num_add m)))
+\ENDTHEOREM
+\THEOREM Sum REAL
+|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
+\ENDTHEOREM
 \THEOREM SUM\_EQ REAL
 |- !N. (!n. N num_le n ==> (f n = g n)) ==> (!n. Sum(N,n)f = Sum(N,n)g)
 \ENDTHEOREM
@@ -1615,8 +1609,7 @@
 \THEOREM SUP\_LEMMA3 REAL
 |- !d. (?z. !x. P x ==> x < z) ==> (?z. !x. (\x. P(x + d))x ==> x < z)
 \ENDTHEOREM
-\section{TOPOLOGY}
-\THEOREM ball TOPOLOGY
+\section{TOPOLOGY}\THEOREM ball TOPOLOGY
 |- !m x e. B m(x,e) = (\y. (dist m(x,y)) < e)
 \ENDTHEOREM
 \THEOREM BALL\_NEIGH TOPOLOGY
@@ -1689,9 +1682,6 @@
 \THEOREM METRIC\_ZERO TOPOLOGY
 |- !m x y. (dist m(x,y) = & 0) = (x = y)
 \ENDTHEOREM
-\THEOREM mr1 TOPOLOGY
-|- mr1 = metric(\(x,y). abs(y - x))
-\ENDTHEOREM
 \THEOREM MR1\_ADD TOPOLOGY
 |- !x d. dist mr1(x,x + d) = abs d
 \ENDTHEOREM
@@ -1707,6 +1697,9 @@
 \THEOREM MR1\_DEF TOPOLOGY
 |- !x y. dist mr1(x,y) = abs(y - x)
 \ENDTHEOREM
+\THEOREM mr1 TOPOLOGY
+|- mr1 = metric(\(x,y). abs(y - x))
+\ENDTHEOREM
 \THEOREM MR1\_LIMPT TOPOLOGY
 |- !x. limpt(mtop mr1)x universe
 \ENDTHEOREM
@@ -1759,12 +1752,12 @@
 \THEOREM OPEN\_UNOPEN TOPOLOGY
 |- !S top. open top S = (Union(\P. open top P /\ P subset S) = S)
 \ENDTHEOREM
-\THEOREM subset TOPOLOGY
-|- !P Q. P subset Q = (!x. P x ==> Q x)
-\ENDTHEOREM
 \THEOREM SUBSET\_ANTISYM TOPOLOGY
 |- !P Q. P subset Q /\ Q subset P = (P = Q)
 \ENDTHEOREM
+\THEOREM subset TOPOLOGY
+|- !P Q. P subset Q = (!x. P x ==> Q x)
+\ENDTHEOREM
 \THEOREM SUBSET\_REFL TOPOLOGY
 |- !S. S subset S
 \ENDTHEOREM
@@ -1788,17 +1781,16 @@
 \THEOREM TOPOLOGY\_UNION TOPOLOGY
 |- !L P. P subset (open L) ==> open L(Union P)
 \ENDTHEOREM
-\THEOREM Union TOPOLOGY
-|- !S. Union S = (\x. ?s. S s /\ s x)
-\ENDTHEOREM
 \THEOREM union\_def TOPOLOGY
 |- !P Q. P union Q = (\x. P x \/ Q x)
 \ENDTHEOREM
+\THEOREM Union TOPOLOGY
+|- !S. Union S = (\x. ?s. S s /\ s x)
+\ENDTHEOREM
 \THEOREM universe TOPOLOGY
 |- universe = (\x. T)
 \ENDTHEOREM
-\section{NETS}
-\THEOREM bounded NETS
+\section{NETS}\THEOREM bounded NETS
 |- !m g f.
     bounded(m,g)f =
     (?k x N. g N N /\ (!n. g n N ==> (dist m(f n,x)) real_lt k))
@@ -1823,7 +1815,7 @@
 \THEOREM DORDER\_TENDSTO NETS
 |- !m x. dorder(tendsto(m,x))
 \ENDTHEOREM
-\THEOREM LIM\_TENDS NETS
+\THEOREM LIM\_TENDS2 NETS
 |- !m1 m2 f x0 y0.
     limpt(mtop m1)x0 universe ==>
     ((f tends y0)(mtop m2,tendsto(m1,x0)) =
@@ -1833,10 +1825,10 @@
          (real_of_num 0) real_lt d /\
          (!x.
            (real_of_num 0) real_lt (dist m1(x,x0)) /\
-           (dist m1(x,x0)) real_le d ==>
+           (dist m1(x,x0)) real_lt d ==>
            (dist m2(f x,y0)) real_lt e))))
 \ENDTHEOREM
-\THEOREM LIM\_TENDS2 NETS
+\THEOREM LIM\_TENDS NETS
 |- !m1 m2 f x0 y0.
     limpt(mtop m1)x0 universe ==>
     ((f tends y0)(mtop m2,tendsto(m1,x0)) =
@@ -1846,7 +1838,7 @@
          (real_of_num 0) real_lt d /\
          (!x.
            (real_of_num 0) real_lt (dist m1(x,x0)) /\
-           (dist m1(x,x0)) real_lt d ==>
+           (dist m1(x,x0)) real_le d ==>
            (dist m2(f x,y0)) real_lt e))))
 \ENDTHEOREM
 \THEOREM MR1\_BOUNDED NETS
@@ -1931,11 +1923,6 @@
       (x tends x0)(mtop mr1,g) =
       ((\n. real_neg(x n)) tends (real_neg x0))(mtop mr1,g))
 \ENDTHEOREM
-\THEOREM NET\_NULL NETS
-|- !g x x0.
-    (x tends x0)(mtop mr1,g) =
-    ((\n. (x n) real_sub x0) tends (real_of_num 0))(mtop mr1,g)
-\ENDTHEOREM
 \THEOREM NET\_NULL\_ADD NETS
 |- !g.
     dorder g ==>
@@ -1949,6 +1936,11 @@
     (x tends (real_of_num 0))(mtop mr1,g) ==>
     ((\n. k real_mul (x n)) tends (real_of_num 0))(mtop mr1,g)
 \ENDTHEOREM
+\THEOREM NET\_NULL NETS
+|- !g x x0.
+    (x tends x0)(mtop mr1,g) =
+    ((\n. (x n) real_sub x0) tends (real_of_num 0))(mtop mr1,g)
+\ENDTHEOREM
 \THEOREM NET\_NULL\_MUL NETS
 |- !g.
     dorder g ==>
@@ -1981,8 +1973,7 @@
     (real_of_num 0) real_lt (dist m(x,y)) /\
     (dist m(x,y)) real_le (dist m(x,z))
 \ENDTHEOREM
-\section{LIM}
-\THEOREM CHAIN\_LEMMA1 LIM
+\section{LIM}\THEOREM CHAIN\_LEMMA1 LIM
 |- !f g x h.
     ((f(g(x + h))) - (f(g x))) / h =
     (((f(g(x + h))) - (f(g x))) / ((g(x + h)) - (g x))) *
@@ -1991,27 +1982,21 @@
 \THEOREM CHAIN\_LEMMA2 LIM
 |- !x y d. (abs(x - y)) < d ==> (abs x) < ((abs y) + d)
 \ENDTHEOREM
-\THEOREM contl LIM
-|- !f x. f contl x = ((\h. f(x + h)) --> (f x))(& 0)
-\ENDTHEOREM
-\THEOREM CONTL\_LIM LIM
-|- !f x. f contl x = (f --> (f x))x
-\ENDTHEOREM
 \THEOREM CONT\_ADD LIM
 |- !x. f contl x /\ g contl x ==> (\x. (f x) + (g x)) contl x
 \ENDTHEOREM
-\THEOREM CONT\_ATTAINS LIM
+\THEOREM CONT\_ATTAINS2 LIM
 |- !f a b.
     a <= b /\ (!x. a <= x /\ x <= b ==> f contl x) ==>
     (?M.
-      (!x. a <= x /\ x <= b ==> (f x) <= M) /\
+      (!x. a <= x /\ x <= b ==> M <= (f x)) /\
       (?x. a <= x /\ x <= b /\ (f x = M)))
 \ENDTHEOREM
-\THEOREM CONT\_ATTAINS2 LIM
+\THEOREM CONT\_ATTAINS LIM
 |- !f a b.
     a <= b /\ (!x. a <= x /\ x <= b ==> f contl x) ==>
     (?M.
-      (!x. a <= x /\ x <= b ==> M <= (f x)) /\
+      (!x. a <= x /\ x <= b ==> (f x) <= M) /\
       (?x. a <= x /\ x <= b /\ (f x = M)))
 \ENDTHEOREM
 \THEOREM CONT\_BOUNDED LIM
@@ -2037,6 +2022,12 @@
 \THEOREM CONT\_INV LIM
 |- !x. f contl x /\ ~(f x = & 0) ==> (\x. inv(f x)) contl x
 \ENDTHEOREM
+\THEOREM contl LIM
+|- !f x. f contl x = ((\h. f(x + h)) --> (f x))(& 0)
+\ENDTHEOREM
+\THEOREM CONTL\_LIM LIM
+|- !f x. f contl x = (f --> (f x))x
+\ENDTHEOREM
 \THEOREM CONT\_MUL LIM
 |- !x. f contl x /\ g contl x ==> (\x. (f x) * (g x)) contl x
 \ENDTHEOREM
@@ -2046,12 +2037,6 @@
 \THEOREM CONT\_SUB LIM
 |- !x. f contl x /\ g contl x ==> (\x. (f x) - (g x)) contl x
 \ENDTHEOREM
-\THEOREM differentiable LIM
-|- !f x. f differentiable x = (?l. (f diffl l)x)
-\ENDTHEOREM
-\THEOREM diffl LIM
-|- !f l x. (f diffl l)x = ((\h. ((f(x + h)) - (f x)) / h) --> l)(& 0)
-\ENDTHEOREM
 \THEOREM DIFF\_ADD LIM
 |- !f g l m x.
     (f diffl l)x /\ (g diffl m)x ==>
@@ -2077,11 +2062,17 @@
      (((l * (g x)) - (m * (f x))) / ((g x) pow 2)))
     x
 \ENDTHEOREM
+\THEOREM differentiable LIM
+|- !f x. f differentiable x = (?l. (f diffl l)x)
+\ENDTHEOREM
 \THEOREM DIFF\_INV LIM
 |- !f l x.
     (f diffl l)x /\ ~(f x = & 0) ==>
     ((\x. inv(f x)) diffl (--(l / ((f x) pow 2))))x
 \ENDTHEOREM
+\THEOREM DIFF\_ISCONST\_ALL LIM
+|- !f. (!x. (f diffl (& 0))x) ==> (!x y. f x = f y)
+\ENDTHEOREM
 \THEOREM DIFF\_ISCONST LIM
 |- !f a b.
     a < b /\
@@ -2089,9 +2080,6 @@
     (!x. a < x /\ x < b ==> (f diffl (& 0))x) ==>
     (!x. a <= x /\ x <= b ==> (f x = f a))
 \ENDTHEOREM
-\THEOREM DIFF\_ISCONST\_ALL LIM
-|- !f. (!x. (f diffl (& 0))x) ==> (!x y. f x = f y)
-\ENDTHEOREM
 \THEOREM DIFF\_ISCONST\_END LIM
 |- !f a b.
     a < b /\
@@ -2110,6 +2098,9 @@
     (f diffl l)x /\ l < (& 0) ==>
     (?d. (& 0) < d /\ (!h. (& 0) < h /\ h < d ==> (f x) < (f(x - h))))
 \ENDTHEOREM
+\THEOREM diffl LIM
+|- !f l x. (f diffl l)x = ((\h. ((f(x + h)) - (f x)) / h) --> l)(& 0)
+\ENDTHEOREM
 \THEOREM DIFF\_LINC LIM
 |- !f x l.
     (f diffl l)x /\ (& 0) < l ==>
@@ -2164,27 +2155,20 @@
     a < x /\ x < b ==>
     (?d. (& 0) < d /\ (!y. (abs(x - y)) < d ==> a <= y /\ y <= b))
 \ENDTHEOREM
-\THEOREM IVT LIM
+\THEOREM IVT2 LIM
 |- !f a b y.
     a <= b /\
-    ((f a) <= y /\ y <= (f b)) /\
+    ((f b) <= y /\ y <= (f a)) /\
     (!x. a <= x /\ x <= b ==> f contl x) ==>
     (?x. a <= x /\ x <= b /\ (f x = y))
 \ENDTHEOREM
-\THEOREM IVT2 LIM
+\THEOREM IVT LIM
 |- !f a b y.
     a <= b /\
-    ((f b) <= y /\ y <= (f a)) /\
+    ((f a) <= y /\ y <= (f b)) /\
     (!x. a <= x /\ x <= b ==> f contl x) ==>
     (?x. a <= x /\ x <= b /\ (f x = y))
 \ENDTHEOREM
-\THEOREM IVT\_SUPLEMMA LIM
-|- a <= b /\
-   ((f a) <= y /\ y <= (f b)) /\
-   (!x. a <= x /\ x <= b ==> f contl x) ==>
-   (?x. (\x. a <= x /\ x <= b /\ (f x) <= y)x) /\
-   (?z. !x. (\x. a <= x /\ x <= b /\ (f x) <= y)x ==> x <= z)
-\ENDTHEOREM
 \THEOREM IVT\_SUPLEMMA2 LIM
 |- a <= b /\
    ((f a) <= y /\ y <= (f b)) /\
@@ -2192,16 +2176,12 @@
    a <= (sup(\x. a <= x /\ x <= b /\ (f x) <= y)) /\
    (sup(\x. a <= x /\ x <= b /\ (f x) <= y)) <= b
 \ENDTHEOREM
-\THEOREM LIM LIM
-|- !f y0 x0.
-    (f --> y0)x0 =
-    (!e.
-      (& 0) < e ==>
-      (?d.
-        (& 0) < d /\
-        (!x.
-          (& 0) < (abs(x - x0)) /\ (abs(x - x0)) < d ==>
-          (abs((f x) - y0)) < e)))
+\THEOREM IVT\_SUPLEMMA LIM
+|- a <= b /\
+   ((f a) <= y /\ y <= (f b)) /\
+   (!x. a <= x /\ x <= b ==> f contl x) ==>
+   (?x. (\x. a <= x /\ x <= b /\ (f x) <= y)x) /\
+   (?z. !x. (\x. a <= x /\ x <= b /\ (f x) <= y)x ==> x <= z)
 \ENDTHEOREM
 \THEOREM LIM\_ADD LIM
 |- !f g l m.
@@ -2221,6 +2201,17 @@
     (f --> l)x /\ (g --> m)x /\ ~(m = & 0) ==>
     ((\x. (f x) / (g x)) --> (l / m))x
 \ENDTHEOREM
+\THEOREM LIM LIM
+|- !f y0 x0.
+    (f --> y0)x0 =
+    (!e.
+      (& 0) < e ==>
+      (?d.
+        (& 0) < d /\
+        (!x.
+          (& 0) < (abs(x - x0)) /\ (abs(x - x0)) < d ==>
+          (abs((f x) - y0)) < e)))
+\ENDTHEOREM
 \THEOREM LIM\_EQUAL LIM
 |- !f g l x0.
     (!x. ~(x = x0) ==> (f x = g x)) ==> ((f --> l)x0 = (g --> l)x0)
@@ -2289,8 +2280,7 @@
 \THEOREM tends\_real\_real LIM
 |- !f l x0. (f --> l)x0 = (f tends l)(mtop mr1,tendsto(mr1,x0))
 \ENDTHEOREM
-\section{SEQ}
-\THEOREM ABS\_NEG\_LEMMA SEQ
+\section{SEQ}\THEOREM ABS\_NEG\_LEMMA SEQ
 |- !c. c <= (& 0) ==> (!x y. (abs x) <= (c * (abs y)) ==> (x = & 0))
 \ENDTHEOREM
 \THEOREM cauchy SEQ
@@ -2326,11 +2316,6 @@
 \THEOREM MONO\_SUC SEQ
 |- !f. mono f = (!n. (f(SUC n)) >= (f n)) \/ (!n. (f(SUC n)) <= (f n))
 \ENDTHEOREM
-\THEOREM SEQ SEQ
-|- !x x0.
-    x --> x0 =
-    (!e. (& 0) < e ==> (?N. !n. n num_ge N ==> (abs((x n) - x0)) < e))
-\ENDTHEOREM
 \THEOREM SEQ\_ABS SEQ
 |- !f. (\n. abs(f n)) --> (& 0) = f --> (& 0)
 \ENDTHEOREM
@@ -2364,18 +2349,23 @@
     x --> x0 /\ y --> y0 /\ ~(y0 = & 0) ==>
     (\n. (x n) / (y n)) --> (x0 / y0)
 \ENDTHEOREM
+\THEOREM SEQ SEQ
+|- !x x0.
+    x --> x0 =
+    (!e. (& 0) < e ==> (?N. !n. n num_ge N ==> (abs((x n) - x0)) < e))
+\ENDTHEOREM
 \THEOREM SEQ\_ICONV SEQ
 |- !f.
     bounded(mr1,$num_ge)f /\ (!m n. m num_ge n ==> (f m) >= (f n)) ==>
     convergent f
 \ENDTHEOREM
-\THEOREM SEQ\_INV SEQ
-|- !x x0. x --> x0 /\ ~(x0 = & 0) ==> (\n. inv(x n)) --> (inv x0)
-\ENDTHEOREM
 \THEOREM SEQ\_INV0 SEQ
 |- !f.
     (!y. ?N. !n. n num_ge N ==> (f n) > y) ==> (\n. inv(f n)) --> (& 0)
 \ENDTHEOREM
+\THEOREM SEQ\_INV SEQ
+|- !x x0. x --> x0 /\ ~(x0 = & 0) ==> (\n. inv(x n)) --> (inv x0)
+\ENDTHEOREM
 \THEOREM SEQ\_LE SEQ
 |- !f g l m.
     f --> l /\ g --> m /\ (?N. !n. n num_ge N ==> (f n) <= (g n)) ==>
@@ -2391,21 +2381,21 @@
 |- !x x0 y y0.
     x --> x0 /\ y --> y0 ==> (\n. (x n) * (y n)) --> (x0 * y0)
 \ENDTHEOREM
-\THEOREM SEQ\_NEG SEQ
-|- !x x0. x --> x0 = (\n. --(x n)) --> (-- x0)
-\ENDTHEOREM
 \THEOREM SEQ\_NEG\_BOUNDED SEQ
 |- !f. bounded(mr1,$num_ge)(\n. --(f n)) = bounded(mr1,$num_ge)f
 \ENDTHEOREM
 \THEOREM SEQ\_NEG\_CONV SEQ
 |- !f. convergent f = convergent(\n. --(f n))
 \ENDTHEOREM
-\THEOREM SEQ\_POWER SEQ
-|- !c. (abs c) < (& 1) ==> (\n. c pow n) --> (& 0)
+\THEOREM SEQ\_NEG SEQ
+|- !x x0. x --> x0 = (\n. --(x n)) --> (-- x0)
 \ENDTHEOREM
 \THEOREM SEQ\_POWER\_ABS SEQ
 |- !c. (abs c) < (& 1) ==> (\n. (abs c) pow n) --> (& 0)
 \ENDTHEOREM
+\THEOREM SEQ\_POWER SEQ
+|- !c. (abs c) < (& 1) ==> (\n. c pow n) --> (& 0)
+\ENDTHEOREM
 \THEOREM SEQ\_SBOUNDED SEQ
 |- !s f. bounded(mr1,$num_ge)s ==> bounded(mr1,$num_ge)(\n. s(f n))
 \ENDTHEOREM
@@ -2447,31 +2437,31 @@
 \THEOREM SER\_CMUL SEQ
 |- !x x0 c. x sums x0 ==> (\n. c * (x n)) sums (c * x0)
 \ENDTHEOREM
-\THEOREM SER\_COMPAR SEQ
+\THEOREM SER\_COMPARA SEQ
 |- !f g.
     (?N. !n. n num_ge N ==> (abs(f n)) <= (g n)) /\ summable g ==>
-    summable f
+    summable(\k. abs(f k))
 \ENDTHEOREM
-\THEOREM SER\_COMPARA SEQ
+\THEOREM SER\_COMPAR SEQ
 |- !f g.
     (?N. !n. n num_ge N ==> (abs(f n)) <= (g n)) /\ summable g ==>
-    summable(\k. abs(f k))
+    summable f
 \ENDTHEOREM
 \THEOREM SER\_GROUP SEQ
 |- !f k.
     summable f /\ 0 num_lt k ==>
     (\n. Sum(n num_mul k,k)f) sums (suminf f)
 \ENDTHEOREM
-\THEOREM SER\_LE SEQ
-|- !f g.
-    (!n. (f n) <= (g n)) /\ summable f /\ summable g ==>
-    (suminf f) <= (suminf g)
-\ENDTHEOREM
 \THEOREM SER\_LE2 SEQ
 |- !f g.
     (!n. (abs(f n)) <= (g n)) /\ summable g ==>
     summable f /\ (suminf f) <= (suminf g)
 \ENDTHEOREM
+\THEOREM SER\_LE SEQ
+|- !f g.
+    (!n. (f n) <= (g n)) /\ summable f /\ summable g ==>
+    (suminf f) <= (suminf g)
+\ENDTHEOREM
 \THEOREM SER\_NEG SEQ
 |- !x x0. x sums x0 ==> (\n. --(x n)) sums (-- x0)
 \ENDTHEOREM
@@ -2542,8 +2532,7 @@
 \THEOREM tends\_num\_real SEQ
 |- !x x0. x --> x0 = (x tends x0)(mtop mr1,$num_ge)
 \ENDTHEOREM
-\section{POWSER}
-\THEOREM diffs POWSER
+\section{POWSER}\THEOREM diffs POWSER
 |- !c. diffs c = (\n. (&(SUC n)) * (c(SUC n)))
 \ENDTHEOREM
 \THEOREM DIFFS\_EQUIV POWSER
@@ -2552,18 +2541,18 @@
     (\n. (& n) * ((c n) * (x pow (n num_sub 1)))) sums
     (suminf(\n. (diffs c n) * (x pow n)))
 \ENDTHEOREM
-\THEOREM DIFFS\_LEMMA POWSER
-|- !n c x.
-    Sum(0,n)(\n'. (diffs c n') * (x pow n')) =
-    (Sum(0,n)(\n'. (& n') * ((c n') * (x pow (n' num_sub 1))))) +
-    ((& n) * ((c n) * (x pow (n num_sub 1))))
-\ENDTHEOREM
 \THEOREM DIFFS\_LEMMA2 POWSER
 |- !n c x.
     Sum(0,n)(\n. (& n) * ((c n) * (x pow (n num_sub 1)))) =
     (Sum(0,n)(\n. (diffs c n) * (x pow n))) -
     ((& n) * ((c n) * (x pow (n num_sub 1))))
 \ENDTHEOREM
+\THEOREM DIFFS\_LEMMA POWSER
+|- !n c x.
+    Sum(0,n)(\n'. (diffs c n') * (x pow n')) =
+    (Sum(0,n)(\n'. (& n') * ((c n') * (x pow (n' num_sub 1))))) +
+    ((& n) * ((c n) * (x pow (n num_sub 1))))
+\ENDTHEOREM
 \THEOREM DIFFS\_NEG POWSER
 |- !c. diffs(\n. --(c n)) = (\n. --(diffs c n))
 \ENDTHEOREM
@@ -2582,15 +2571,15 @@
     Sum(0,SUC n)(\p. (x pow p) * (y pow (n num_sub p))) =
     Sum(0,SUC n)(\p. (x pow (n num_sub p)) * (y pow p))
 \ENDTHEOREM
-\THEOREM POWSER\_INSIDE POWSER
+\THEOREM POWSER\_INSIDEA POWSER
 |- !f x z.
     summable(\n. (f n) * (x pow n)) /\ (abs z) < (abs x) ==>
-    summable(\n. (f n) * (z pow n))
+    summable(\n. (abs(f n)) * (z pow n))
 \ENDTHEOREM
-\THEOREM POWSER\_INSIDEA POWSER
+\THEOREM POWSER\_INSIDE POWSER
 |- !f x z.
     summable(\n. (f n) * (x pow n)) /\ (abs z) < (abs x) ==>
-    summable(\n. (abs(f n)) * (z pow n))
+    summable(\n. (f n) * (z pow n))
 \ENDTHEOREM
 \THEOREM TERMDIFF POWSER
 |- !c K.
@@ -2649,69 +2638,58 @@
       (!n. (abs(g h n)) <= ((f n) * (abs h)))) ==>
     ((\h. suminf(g h)) tends_real_real (& 0))(& 0)
 \ENDTHEOREM
-\section{TRANSC}
-\THEOREM ACS TRANSC
+\section{TRANSC}\THEOREM ACS\_BOUNDS TRANSC
 |- !y.
-    (--(& 1)) <= y /\ y <= (& 1) ==>
-    (& 0) <= (acs y) /\ (acs y) <= pi /\ (cos(acs y) = y)
+    (--(& 1)) <= y /\ y <= (& 1) ==> (& 0) <= (acs y) /\ (acs y) <= pi
+\ENDTHEOREM
+\THEOREM ACS\_COS TRANSC
+|- !y. (--(& 1)) <= y /\ y <= (& 1) ==> (cos(acs y) = y)
 \ENDTHEOREM
 \THEOREM acs TRANSC
 |- !y. acs y = (@x. (& 0) <= x /\ x <= pi /\ (cos x = y))
 \ENDTHEOREM
-\THEOREM ACS\_BOUNDS TRANSC
+\THEOREM ACS TRANSC
 |- !y.
-    (--(& 1)) <= y /\ y <= (& 1) ==> (& 0) <= (acs y) /\ (acs y) <= pi
-\ENDTHEOREM
-\THEOREM ACS\_COS TRANSC
-|- !y. (--(& 1)) <= y /\ y <= (& 1) ==> (cos(acs y) = y)
+    (--(& 1)) <= y /\ y <= (& 1) ==>
+    (& 0) <= (acs y) /\ (acs y) <= pi /\ (cos(acs y) = y)
 \ENDTHEOREM
-\THEOREM ASN TRANSC
+\THEOREM ASN\_BOUNDS TRANSC
 |- !y.
     (--(& 1)) <= y /\ y <= (& 1) ==>
-    (--(pi / (& 2))) <= (asn y) /\
-    (asn y) <= (pi / (& 2)) /\
-    (sin(asn y) = y)
+    (--(pi / (& 2))) <= (asn y) /\ (asn y) <= (pi / (& 2))
 \ENDTHEOREM
 \THEOREM asn TRANSC
 |- !y.
     asn y =
     (@x. (--(pi / (& 2))) <= x /\ x <= (pi / (& 2)) /\ (sin x = y))
 \ENDTHEOREM
-\THEOREM ASN\_BOUNDS TRANSC
+\THEOREM ASN TRANSC
 |- !y.
     (--(& 1)) <= y /\ y <= (& 1) ==>
-    (--(pi / (& 2))) <= (asn y) /\ (asn y) <= (pi / (& 2))
+    (--(pi / (& 2))) <= (asn y) /\
+    (asn y) <= (pi / (& 2)) /\
+    (sin(asn y) = y)
 \ENDTHEOREM
 \THEOREM ASN\_SIN TRANSC
 |- !y. (--(& 1)) <= y /\ y <= (& 1) ==> (sin(asn y) = y)
 \ENDTHEOREM
-\THEOREM ATN TRANSC
-|- !y.
-    (--(pi / (& 2))) < (atn y) /\
-    (atn y) < (pi / (& 2)) /\
-    (tan(atn y) = y)
+\THEOREM ATN\_BOUNDS TRANSC
+|- !y. (--(pi / (& 2))) < (atn y) /\ (atn y) < (pi / (& 2))
 \ENDTHEOREM
 \THEOREM atn TRANSC
 |- !y.
     atn y =
     (@x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) /\ (tan x = y))
 \ENDTHEOREM
-\THEOREM ATN\_BOUNDS TRANSC
-|- !y. (--(pi / (& 2))) < (atn y) /\ (atn y) < (pi / (& 2))
+\THEOREM ATN TRANSC
+|- !y.
+    (--(pi / (& 2))) < (atn y) /\
+    (atn y) < (pi / (& 2)) /\
+    (tan(atn y) = y)
 \ENDTHEOREM
 \THEOREM ATN\_TAN TRANSC
 |- !y. tan(atn y) = y
 \ENDTHEOREM
-\THEOREM cos TRANSC
-|- !x.
-    cos x =
-    suminf
-    (\n.
-      ((\n'.
-         (EVEN n' => ((--(& 1)) pow (n' DIV 2)) / (&(FACT n')) | & 0))
-       n) *
-      (x pow n))
-\ENDTHEOREM
 \THEOREM COS\_0 TRANSC
 |- cos(& 0) = & 1
 \ENDTHEOREM
@@ -2737,6 +2715,16 @@
       (x pow n)) sums
     (cos x)
 \ENDTHEOREM
+\THEOREM cos TRANSC
+|- !x.
+    cos x =
+    suminf
+    (\n.
+      ((\n'.
+         (EVEN n' => ((--(& 1)) pow (n' DIV 2)) / (&(FACT n')) | & 0))
+       n) *
+      (x pow n))
+\ENDTHEOREM
 \THEOREM COS\_DOUBLE TRANSC
 |- !x. cos((& 2) * x) = ((cos x) pow 2) - ((sin x) pow 2)
 \ENDTHEOREM
@@ -2772,18 +2760,18 @@
 \THEOREM COS\_PERIODIC\_PI TRANSC
 |- !x. cos(x + pi) = --(cos x)
 \ENDTHEOREM
-\THEOREM COS\_PI TRANSC
-|- cos pi = --(& 1)
-\ENDTHEOREM
 \THEOREM COS\_PI2 TRANSC
 |- cos(pi / (& 2)) = & 0
 \ENDTHEOREM
-\THEOREM COS\_POS\_PI TRANSC
-|- !x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) ==> (& 0) < (cos x)
+\THEOREM COS\_PI TRANSC
+|- cos pi = --(& 1)
 \ENDTHEOREM
 \THEOREM COS\_POS\_PI2 TRANSC
 |- !x. (& 0) < x /\ x < (pi / (& 2)) ==> (& 0) < (cos x)
 \ENDTHEOREM
+\THEOREM COS\_POS\_PI TRANSC
+|- !x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) ==> (& 0) < (cos x)
+\ENDTHEOREM
 \THEOREM COS\_SIN TRANSC
 |- !x. cos x = sin((pi / (& 2)) - x)
 \ENDTHEOREM
@@ -2815,9 +2803,6 @@
 \THEOREM DIFF\_TAN TRANSC
 |- !x. ~(cos x = & 0) ==> (tan diffl (inv((cos x) pow 2)))x
 \ENDTHEOREM
-\THEOREM exp TRANSC
-|- !x. exp x = suminf(\n. ((\n'. inv(&(FACT n')))n) * (x pow n))
-\ENDTHEOREM
 \THEOREM EXP\_0 TRANSC
 |- exp(& 0) = & 1
 \ENDTHEOREM
@@ -2830,6 +2815,9 @@
 \THEOREM EXP\_CONVERGES TRANSC
 |- !x. (\n. ((\n. inv(&(FACT n)))n) * (x pow n)) sums (exp x)
 \ENDTHEOREM
+\THEOREM exp TRANSC
+|- !x. exp x = suminf(\n. ((\n'. inv(&(FACT n')))n) * (x pow n))
+\ENDTHEOREM
 \THEOREM EXP\_FDIFF TRANSC
 |- diffs(\n. inv(&(FACT n))) = (\n. inv(&(FACT n)))
 \ENDTHEOREM
@@ -2860,12 +2848,12 @@
 \THEOREM EXP\_NEG TRANSC
 |- !x. exp(-- x) = inv(exp x)
 \ENDTHEOREM
-\THEOREM EXP\_NEG\_MUL TRANSC
-|- !x. (exp x) * (exp(-- x)) = & 1
-\ENDTHEOREM
 \THEOREM EXP\_NEG\_MUL2 TRANSC
 |- !x. (exp(-- x)) * (exp x) = & 1
 \ENDTHEOREM
+\THEOREM EXP\_NEG\_MUL TRANSC
+|- !x. (exp x) * (exp(-- x)) = & 1
+\ENDTHEOREM
 \THEOREM EXP\_NZ TRANSC
 |- !x. ~(exp x = & 0)
 \ENDTHEOREM
@@ -2885,15 +2873,15 @@
 |- !y.
     (& 1) <= y ==> (?x. (& 0) <= x /\ x <= (y - (& 1)) /\ (exp x = y))
 \ENDTHEOREM
-\THEOREM ln TRANSC
-|- !x. ln x = (@u. exp u = x)
-\ENDTHEOREM
 \THEOREM LN\_1 TRANSC
 |- ln(& 1) = & 0
 \ENDTHEOREM
 \THEOREM LN\_DIV TRANSC
 |- !x. (& 0) < x /\ (& 0) < y ==> (ln(x / y) = (ln x) - (ln y))
 \ENDTHEOREM
+\THEOREM ln TRANSC
+|- !x. ln x = (@u. exp u = x)
+\ENDTHEOREM
 \THEOREM LN\_EXP TRANSC
 |- !x. ln(exp x) = x
 \ENDTHEOREM
@@ -2915,27 +2903,27 @@
 \THEOREM LN\_POW TRANSC
 |- !n x. (& 0) < x ==> (ln(x pow n) = (& n) * (ln x))
 \ENDTHEOREM
-\THEOREM pi TRANSC
-|- pi = (& 2) * (@x. (& 0) <= x /\ x <= (& 2) /\ (cos x = & 0))
+\THEOREM PI2\_BOUNDS TRANSC
+|- (& 0) < (pi / (& 2)) /\ (pi / (& 2)) < (& 2)
 \ENDTHEOREM
 \THEOREM PI2 TRANSC
 |- pi / (& 2) = (@x. (& 0) <= x /\ x <= (& 2) /\ (cos x = & 0))
 \ENDTHEOREM
-\THEOREM PI2\_BOUNDS TRANSC
-|- (& 0) < (pi / (& 2)) /\ (pi / (& 2)) < (& 2)
+\THEOREM pi TRANSC
+|- pi = (& 2) * (@x. (& 0) <= x /\ x <= (& 2) /\ (cos x = & 0))
 \ENDTHEOREM
 \THEOREM PI\_POS TRANSC
 |- (& 0) < pi
 \ENDTHEOREM
-\THEOREM root TRANSC
-|- !n x. root n x = (@u. ((& 0) < x ==> (& 0) < u) /\ (u pow n = x))
-\ENDTHEOREM
 \THEOREM ROOT\_0 TRANSC
 |- !n. root(SUC n)(& 0) = & 0
 \ENDTHEOREM
 \THEOREM ROOT\_1 TRANSC
 |- !n. root(SUC n)(& 1) = & 1
 \ENDTHEOREM
+\THEOREM root TRANSC
+|- !n x. root n x = (@u. ((& 0) < x ==> (& 0) < u) /\ (u pow n = x))
+\ENDTHEOREM
 \THEOREM ROOT\_LN TRANSC
 |- !n x. (& 0) < x ==> (!n. root(SUC n)x = exp((ln x) / (&(SUC n))))
 \ENDTHEOREM
@@ -2945,18 +2933,6 @@
 \THEOREM ROOT\_POW\_POS TRANSC
 |- !n x. (& 0) <= x ==> ((root(SUC n)x) pow (SUC n) = x)
 \ENDTHEOREM
-\THEOREM sin TRANSC
-|- !x.
-    sin x =
-    suminf
-    (\n.
-      ((\n'.
-         (EVEN n' =>
-          & 0 |
-          ((--(& 1)) pow ((n' num_sub 1) DIV 2)) / (&(FACT n'))))
-       n) *
-      (x pow n))
-\ENDTHEOREM
 \THEOREM SIN\_0 TRANSC
 |- sin(& 0) = & 0
 \ENDTHEOREM
@@ -2986,20 +2962,32 @@
       (x pow n)) sums
     (sin x)
 \ENDTHEOREM
-\THEOREM SIN\_COS TRANSC
-|- !x. sin x = cos((pi / (& 2)) - x)
-\ENDTHEOREM
 \THEOREM SIN\_COS\_ADD TRANSC
 |- !x y.
     (((sin(x + y)) - (((sin x) * (cos y)) + ((cos x) * (sin y)))) pow 2) +
     (((cos(x + y)) - (((cos x) * (cos y)) - ((sin x) * (sin y)))) pow 2) =
     & 0
 \ENDTHEOREM
+\THEOREM SIN\_COS TRANSC
+|- !x. sin x = cos((pi / (& 2)) - x)
+\ENDTHEOREM
 \THEOREM SIN\_COS\_NEG TRANSC
 |- !x.
     (((sin(-- x)) + (sin x)) pow 2) + (((cos(-- x)) - (cos x)) pow 2) =
     & 0
 \ENDTHEOREM
+\THEOREM sin TRANSC
+|- !x.
+    sin x =
+    suminf
+    (\n.
+      ((\n'.
+         (EVEN n' =>
+          & 0 |
+          ((--(& 1)) pow ((n' num_sub 1) DIV 2)) / (&(FACT n'))))
+       n) *
+      (x pow n))
+\ENDTHEOREM
 \THEOREM SIN\_DOUBLE TRANSC
 |- !x. sin((& 2) * x) = (& 2) * ((sin x) * (cos x))
 \ENDTHEOREM
@@ -3043,21 +3031,21 @@
 \THEOREM SIN\_PERIODIC\_PI TRANSC
 |- !x. sin(x + pi) = --(sin x)
 \ENDTHEOREM
-\THEOREM SIN\_PI TRANSC
-|- sin pi = & 0
-\ENDTHEOREM
 \THEOREM SIN\_PI2 TRANSC
 |- sin(pi / (& 2)) = & 1
 \ENDTHEOREM
+\THEOREM SIN\_PI TRANSC
+|- sin pi = & 0
+\ENDTHEOREM
 \THEOREM SIN\_POS TRANSC
 |- !x. (& 0) < x /\ x < (& 2) ==> (& 0) < (sin x)
 \ENDTHEOREM
-\THEOREM SIN\_POS\_PI TRANSC
-|- !x. (& 0) < x /\ x < pi ==> (& 0) < (sin x)
-\ENDTHEOREM
 \THEOREM SIN\_POS\_PI2 TRANSC
 |- !x. (& 0) < x /\ x < (pi / (& 2)) ==> (& 0) < (sin x)
 \ENDTHEOREM
+\THEOREM SIN\_POS\_PI TRANSC
+|- !x. (& 0) < x /\ x < pi ==> (& 0) < (sin x)
+\ENDTHEOREM
 \THEOREM SIN\_TOTAL TRANSC
 |- !y.
     (--(& 1)) <= y /\ y <= (& 1) ==>
@@ -3074,21 +3062,18 @@
     (& 0) <= x /\ (sin x = & 0) ==>
     (?n. EVEN n /\ (x = (& n) * (pi / (& 2))))
 \ENDTHEOREM
-\THEOREM sqrt TRANSC
-|- !x. sqrt x = root 2 x
-\ENDTHEOREM
 \THEOREM SQRT\_0 TRANSC
 |- sqrt(& 0) = & 0
 \ENDTHEOREM
 \THEOREM SQRT\_1 TRANSC
 |- sqrt(& 1) = & 1
 \ENDTHEOREM
+\THEOREM sqrt TRANSC
+|- !x. sqrt x = root 2 x
+\ENDTHEOREM
 \THEOREM SQRT\_POW2 TRANSC
 |- !x. ((sqrt x) pow 2 = x) = (& 0) <= x
 \ENDTHEOREM
-\THEOREM tan TRANSC
-|- !x. tan x = (sin x) / (cos x)
-\ENDTHEOREM
 \THEOREM TAN\_0 TRANSC
 |- tan(& 0) = & 0
 \ENDTHEOREM
@@ -3100,6 +3085,9 @@
 \THEOREM TAN\_ATN TRANSC
 |- !x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) ==> (atn(tan x) = x)
 \ENDTHEOREM
+\THEOREM tan TRANSC
+|- !x. tan x = (sin x) / (cos x)
+\ENDTHEOREM
 \THEOREM TAN\_DOUBLE TRANSC
 |- !x.
     ~(cos x = & 0) /\ ~(cos((& 2) * x) = & 0) ==>
--- hol88-2.02.19940316.orig/Library/parser/Manual/entries.tex
+++ hol88-2.02.19940316/Library/parser/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the parser Library}
-\input{entries-intro}
-\DOC{parse}
+\chapter{ML Functions in the parser Library}\input{entries-intro}\DOC{parse}
 
 \TYPE {\small\verb%parse : (* -> void)%}\egroup
 
--- hol88-2.02.19940316.orig/Library/parser/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/parser/Manual/theorems.tex
@@ -1 +1 @@
-\chapter{Pre-proved Theorems}
+\chapter{Pre-proved Theorems}
\ No newline at end of file
--- hol88-2.02.19940316.orig/Library/unwind/Manual/entries.tex
+++ hol88-2.02.19940316/Library/unwind/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the unwind Library}
-\input{entries-intro}
-\DOC{CONJ\_FORALL\_CONV}
+\chapter{ML Functions in the unwind Library}\input{entries-intro}\DOC{CONJ\_FORALL\_CONV}
 
 \TYPE {\small\verb%CONJ_FORALL_CONV : conv%}\egroup
 
--- hol88-2.02.19940316.orig/Library/string/Manual/entries.tex
+++ hol88-2.02.19940316/Library/string/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the string Library}
-\input{entries-intro}
-\DOC{ascii\_EQ\_CONV}
+\chapter{ML Functions in the string Library}\input{entries-intro}\DOC{ascii\_EQ\_CONV}
 
 \TYPE {\small\verb%ascii_EQ_CONV : conv%}\egroup
 
--- hol88-2.02.19940316.orig/Library/string/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/string/Manual/theorems.tex
@@ -1,7 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{Definitions}
-\THEOREM ASCII\_DEF ascii
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{Definitions}\THEOREM ASCII\_DEF ascii
 |- !b0 b1 b2 b3 b4 b5 b6 b7.
     ASCII b0 b1 b2 b3 b4 b5 b6 b7 =
     ABS_ascii(Node(b0,b1,b2,b3,b4,b5,b6,b7)[])
@@ -25,6 +22,9 @@
        (LENGTH tl = 0)))
     rep
 \ENDTHEOREM
+\THEOREM ``\_DEF string
+|- `` = ABS_string(Node(INL one)[]))
+\ENDTHEOREM
 \THEOREM STRING\_DEF string
 |- !a s. STRING a s = ABS_string(Node(INR a)[REP_string s])
 \ENDTHEOREM
@@ -47,11 +47,7 @@
        (?a. v = INR a) /\ (LENGTH tl = SUC 0)))
     rep
 \ENDTHEOREM
-\THEOREM ``\_DEF string
-|- `` = ABS_string(Node(INL one)[]))
-\ENDTHEOREM
-\section{Theorems}
-\THEOREM ASCII\_11 ascii
+\section{Theorems}\THEOREM ASCII\_11 ascii
 |- !b0 b1 b2 b3 b4 b5 b6 b7 b0' b1' b2' b3' b4' b5' b6' b7'.
     (ASCII b0 b1 b2 b3 b4 b5 b6 b7 =
      ASCII b0' b1' b2' b3' b4' b5' b6' b7') =
--- hol88-2.02.19940316.orig/Library/wellorder/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/wellorder/Manual/theorems.tex
@@ -1,7 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{Basic definitions}
-\THEOREM wo\_chain WELLORDER
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{Basic definitions}\THEOREM wo\_chain WELLORDER
 |- !l P. chain l P = (!x y. P x /\ P y ==> l(x,y) \/ l(y,x))
 \ENDTHEOREM
 \THEOREM wo\_fl WELLORDER
@@ -41,8 +38,7 @@
       (!x. P x ==> fl l x) /\ (?x. P x) ==>
       (?y. P y /\ (!z. P z ==> l(y,z))))
 \ENDTHEOREM
-\section{Miscellaneous lemmas}
-\THEOREM AGREE\_LEMMA WELLORDER
+\section{Miscellaneous lemmas}\THEOREM AGREE\_LEMMA WELLORDER
 |- !l h ms m n f g z.
     woset l /\
     (!x. fl l(ms x)) /\
@@ -152,44 +148,6 @@
 \THEOREM UNION\_INSEG WELLORDER
 |- !P l. (!m. P m ==> m inseg l) ==> (Union P) inseg l
 \ENDTHEOREM
-\THEOREM WOSET WELLORDER
-|- !l.
-    woset l =
-    (!x y. l(x,y) /\ l(y,x) ==> (x = y)) /\
-    (!P.
-      (!x. P x ==> fl l x) /\ (?x. P x) ==>
-      (?y. P y /\ (!z. P z ==> l(y,z))))
-\ENDTHEOREM
-\THEOREM WOSET\_FLEQ WELLORDER
-|- !l. woset l ==> (!x. fl l x = l(x,x))
-\ENDTHEOREM
-\THEOREM WOSET\_NUM WELLORDER
-|- woset(\(m,n). m <= n)
-\ENDTHEOREM
-\THEOREM WOSET\_POSET WELLORDER
-|- !l. woset l ==> poset l
-\ENDTHEOREM
-\THEOREM WOSET\_TOTAL\_LE WELLORDER
-|- !l. woset l ==> (!x y. fl l x /\ fl l y ==> l(x,y) \/ less l(y,x))
-\ENDTHEOREM
-\THEOREM WOSET\_TOTAL\_LT WELLORDER
-|- !l.
-    woset l ==>
-    (!x y. fl l x /\ fl l y ==> (x = y) \/ less l(x,y) \/ less l(y,x))
-\ENDTHEOREM
-\THEOREM WOSET\_TRANS\_LE WELLORDER
-|- !l. woset l ==> (!x y z. l(x,y) /\ less l(y,z) ==> less l(x,z))
-\ENDTHEOREM
-\THEOREM WOSET\_TRANS\_LESS WELLORDER
-|- !l. woset l ==> (!x y z. less l(x,y) /\ l(y,z) ==> less l(x,z))
-\ENDTHEOREM
-\THEOREM WOSET\_WELL\_CONTRAPOS WELLORDER
-|- !l.
-    woset l ==>
-    (!P.
-      (!x. P x ==> fl l x) /\ (?x. P x) ==>
-      (?y. P y /\ (!z. less l(z,y) ==> ~P z)))
-\ENDTHEOREM
 \THEOREM WO\_FL\_RESTRICT WELLORDER
 |- !l.
     woset l ==>
@@ -233,8 +191,45 @@
       (!y. (ms y) < (ms x) ==> (f y = g y)) ==> (h f x = h g x)) ==>
     (?! f. !x. f x = h f x)
 \ENDTHEOREM
-\section{Main theorems}
-\THEOREM HP WELLORDER
+\THEOREM WOSET WELLORDER
+|- !l.
+    woset l =
+    (!x y. l(x,y) /\ l(y,x) ==> (x = y)) /\
+    (!P.
+      (!x. P x ==> fl l x) /\ (?x. P x) ==>
+      (?y. P y /\ (!z. P z ==> l(y,z))))
+\ENDTHEOREM
+\THEOREM WOSET\_FLEQ WELLORDER
+|- !l. woset l ==> (!x. fl l x = l(x,x))
+\ENDTHEOREM
+\THEOREM WOSET\_NUM WELLORDER
+|- woset(\(m,n). m <= n)
+\ENDTHEOREM
+\THEOREM WOSET\_POSET WELLORDER
+|- !l. woset l ==> poset l
+\ENDTHEOREM
+\THEOREM WOSET\_TOTAL\_LE WELLORDER
+|- !l. woset l ==> (!x y. fl l x /\ fl l y ==> l(x,y) \/ less l(y,x))
+\ENDTHEOREM
+\THEOREM WOSET\_TOTAL\_LT WELLORDER
+|- !l.
+    woset l ==>
+    (!x y. fl l x /\ fl l y ==> (x = y) \/ less l(x,y) \/ less l(y,x))
+\ENDTHEOREM
+\THEOREM WOSET\_TRANS\_LE WELLORDER
+|- !l. woset l ==> (!x y z. l(x,y) /\ less l(y,z) ==> less l(x,z))
+\ENDTHEOREM
+\THEOREM WOSET\_TRANS\_LESS WELLORDER
+|- !l. woset l ==> (!x y z. less l(x,y) /\ l(y,z) ==> less l(x,z))
+\ENDTHEOREM
+\THEOREM WOSET\_WELL\_CONTRAPOS WELLORDER
+|- !l.
+    woset l ==>
+    (!P.
+      (!x. P x ==> fl l x) /\ (?x. P x) ==>
+      (?y. P y /\ (!z. less l(z,y) ==> ~P z)))
+\ENDTHEOREM
+\section{Main theorems}\THEOREM HP WELLORDER
 |- !l.
     poset l ==>
     (?P. chain l P /\ (!Q. chain l Q /\ P subset Q ==> (Q = P)))
--- hol88-2.02.19940316.orig/Library/record_proof/Manual/entries.tex
+++ hol88-2.02.19940316/Library/record_proof/Manual/entries.tex
@@ -1,3 +1 @@
-\chapter{ML Functions in the {\tt record\_proof} Library}
-\label{entries}
-\input{entries-intro}
+\chapter{ML Functions in the {\tt record\_proof} Library}\label{entries}\input{entries-intro}
\ No newline at end of file
--- hol88-2.02.19940316.orig/Library/arith/Manual/entries.tex
+++ hol88-2.02.19940316/Library/arith/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the arith Library}
-\input{entries-intro}
-\DOC{ARITH\_CONV}
+\chapter{ML Functions in the arith Library}\input{entries-intro}\DOC{ARITH\_CONV}
 
 \TYPE {\small\verb%ARITH_CONV : conv%}\egroup
 
--- hol88-2.02.19940316.orig/Library/taut/Manual/entries.tex
+++ hol88-2.02.19940316/Library/taut/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the taut Library}
-\input{entries-intro}
-\DOC{PTAUT\_CONV}
+\chapter{ML Functions in the taut Library}\input{entries-intro}\DOC{PTAUT\_CONV}
 
 \TYPE {\small\verb%PTAUT_CONV : conv%}\egroup
 
--- hol88-2.02.19940316.orig/Library/prettyp/Manual/entries.tex
+++ hol88-2.02.19940316/Library/prettyp/Manual/entries.tex
@@ -1,6 +1,4 @@
-\chapter{ML Functions in the prettyp Library}
-\input{entries-intro}
-\DOC{Address}
+\chapter{ML Functions in the prettyp Library}\input{entries-intro}\DOC{Address}
 
 \TYPE {\small\verb%Address : (int list -> address)%}\egroup
 
@@ -831,57 +829,6 @@
 Hidden_types, Useful_types, All_types, term_to_print_tree.
 
 \ENDDOC
-\DOC{pp}
-
-{\small
-\begin{verbatim}
-pp : (print_rule_function -> string -> (string # int) list ->
-      print_tree -> void)
-\end{verbatim}
-}\egroup
-
-\SYNOPSIS
-One of the main pretty-printing functions. For use with the standard HOL
-pretty-printer.
-
-\DESCRIBE
-{\small\verb%pp%} invokes the pretty-printer. It can be used for merging output with text
-produced by the standard HOL pretty-printer. Instead of ending each line of
-text by printing a new-line, it sends its output to the standard HOL printer
-in the form of a pretty-printing block. The arguments to the function are:
-(1) pretty-printing rules expressed as a function, (2) the initial context,
-(3) initial parameters, (4) tree to be printed. {\small\verb%pp%} uses as its maximum width
-the width for the standard HOL printer, as specified by the function
-{\small\verb%set_margin%}. The initial offset from the left margin is taken to be zero.
-
-\FAILURE
-Failure or incorrect behaviour can be caused by mistakes in the pretty-printing
-rules or by inappropriate arguments to the printing function. The most common
-errors are use of uninitialised parameters and reference to unknown
-metavariables. The latter are due to metavariables appearing in the format of a
-rule, but not in the pattern. Errors also occur if a metavariable is used in a
-place inappropriate for the value it is bound to. An example of this is an
-attempt to compare a string with a metavariable that is bound to a tree rather
-than a node-name.
-
-Use of negative indentations in formats may cause text to overflow the left
-margin, and an exception to be raised. Any user defined function may also
-cause a run-time error.
-
-The printing functions have been designed to trap exceptions and to print
-{\small\verb%*error*%}. This does not indicate what caused the error, but it may give some
-indication of where the error occurred. However, this is not the main reason
-for trapping exceptions. The ML directive {\small\verb%top_print%} installs a user print
-function. If an exception is raised within this function, it does not appear
-at the top-level of ML. Instead, an obscure Lisp error is produced. Since the
-pretty-printing functions are normally used with {\small\verb%top_print%}, it is best to
-avoid raising exceptions. For this reason the printing functions display
-{\small\verb%*error*%} instead.
-
-\SEEALSO
-pretty_print, pp_write.
-
-\ENDDOC
 \DOC{pp\_convert\_all\_thm}
 
 \TYPE {\small\verb%pp_convert_all_thm : (thm -> print_tree)%}\egroup
@@ -991,6 +938,57 @@
 type_to_print_tree, pp_convert_term, pp_convert_thm, pp_convert_all_thm.
 
 \ENDDOC
+\DOC{pp}
+
+{\small
+\begin{verbatim}
+pp : (print_rule_function -> string -> (string # int) list ->
+      print_tree -> void)
+\end{verbatim}
+}\egroup
+
+\SYNOPSIS
+One of the main pretty-printing functions. For use with the standard HOL
+pretty-printer.
+
+\DESCRIBE
+{\small\verb%pp%} invokes the pretty-printer. It can be used for merging output with text
+produced by the standard HOL pretty-printer. Instead of ending each line of
+text by printing a new-line, it sends its output to the standard HOL printer
+in the form of a pretty-printing block. The arguments to the function are:
+(1) pretty-printing rules expressed as a function, (2) the initial context,
+(3) initial parameters, (4) tree to be printed. {\small\verb%pp%} uses as its maximum width
+the width for the standard HOL printer, as specified by the function
+{\small\verb%set_margin%}. The initial offset from the left margin is taken to be zero.
+
+\FAILURE
+Failure or incorrect behaviour can be caused by mistakes in the pretty-printing
+rules or by inappropriate arguments to the printing function. The most common
+errors are use of uninitialised parameters and reference to unknown
+metavariables. The latter are due to metavariables appearing in the format of a
+rule, but not in the pattern. Errors also occur if a metavariable is used in a
+place inappropriate for the value it is bound to. An example of this is an
+attempt to compare a string with a metavariable that is bound to a tree rather
+than a node-name.
+
+Use of negative indentations in formats may cause text to overflow the left
+margin, and an exception to be raised. Any user defined function may also
+cause a run-time error.
+
+The printing functions have been designed to trap exceptions and to print
+{\small\verb%*error*%}. This does not indicate what caused the error, but it may give some
+indication of where the error occurred. However, this is not the main reason
+for trapping exceptions. The ML directive {\small\verb%top_print%} installs a user print
+function. If an exception is raised within this function, it does not appear
+at the top-level of ML. Instead, an obscure Lisp error is produced. Since the
+pretty-printing functions are normally used with {\small\verb%top_print%}, it is best to
+avoid raising exceptions. For this reason the printing functions display
+{\small\verb%*error*%} instead.
+
+\SEEALSO
+pretty_print, pp_write.
+
+\ENDDOC
 \DOC{pp\_print\_all\_thm}
 
 \TYPE {\small\verb%pp_print_all_thm : (thm -> void)%}\egroup
--- hol88-2.02.19940316.orig/Library/finite_sets/Manual/entries.tex
+++ hol88-2.02.19940316/Library/finite_sets/Manual/entries.tex
@@ -1,7 +1,4 @@
-\chapter{ML Functions in the Library}
-\label{entries}
-\input{entries-intro}
-\DOC{DELETE\_CONV}
+\chapter{ML Functions in the Library}\label{entries}\input{entries-intro}\DOC{DELETE\_CONV}
 
 \TYPE {\small\verb%DELETE_CONV : conv -> conv%}\egroup
 
@@ -171,6 +168,84 @@
 
 \ENDDOC
 
+\DOC{IN\_CONV}
+
+\TYPE {\small\verb%IN_CONV : conv -> conv%}\egroup
+
+\SYNOPSIS
+Decision procedure for membership in finite sets.
+
+\DESCRIBE 
+The function {\small\verb%IN_CONV%} is a parameterized conversion for proving or disproving
+membership assertions of the general form:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   "t IN {t1,...,tn}"
+\end{verbatim}
+}
+\noindent where {\small\verb%{t1,...,tn}%} is a set of type {\small\verb%(ty)set%} and {\small\verb%t%} is a value
+of the base type {\small\verb%ty%}.  The first argument to {\small\verb%IN_CONV%} is expected to be a
+conversion that decides equality between values of the base type {\small\verb%ty%}.  Given
+an equation {\small\verb%"e1 = e2"%}, where {\small\verb%e1%} and {\small\verb%e2%} are terms of type {\small\verb%ty%}, this
+conversion should return the theorem {\small\verb%|- (e1 = e2) = T%} or the theorem
+{\small\verb%|- (e1 = e2) = F%}, as appropriate.
+
+Given such a conversion, the function {\small\verb%IN_CONV%} returns a conversion that
+maps a term of the form {\small\verb%"t IN {t1,...,tn}"%} to the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- t IN {t1,...,tn} = T
+\end{verbatim}
+}
+
+\noindent if {\small\verb%t%} is alpha-equivalent to any {\small\verb%ti%}, or if the supplied conversion
+proves {\small\verb%|- (t = ti) = T%} for any {\small\verb%ti%}. If the supplied conversion proves
+{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}, then the result is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- t IN {t1,...,tn} = F 
+\end{verbatim}
+}
+\noindent In all other cases, {\small\verb%IN_CONV%} will fail.
+
+\EXAMPLE
+In the following example, the conversion {\small\verb%num_EQ_CONV%} is supplied as a
+parameter and used to test equality of the candidate element {\small\verb%1%} with the
+actual elements of the given set.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV num_EQ_CONV "2 IN {0,SUC 1,3}";;
+   |- 2 IN {0,SUC 1,3} = T
+\end{verbatim}
+}
+\noindent The result is {\small\verb%T%} because {\small\verb%num_EQ_CONV%} is able to prove that {\small\verb%2%} is
+equal to {\small\verb%SUC 1%}. An example of a negative result is:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV num_EQ_CONV "1 IN {0,2,3}";;
+   |- 1 IN {0,2,3} = F
+\end{verbatim}
+}
+\noindent Finally the behaviour of the supplied conversion is irrelevant when
+the value to be tested for membership is alpha-equivalent to an actual element:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV NO_CONV "1 IN {3,2,1}";;
+   |- 1 IN {3,2,1} = T
+\end{verbatim}
+}
+\noindent The conversion {\small\verb%NO_CONV%} always fails, but {\small\verb%IN_CONV%} is nontheless
+able in this case to prove the required result.
+
+\FAILURE
+{\small\verb%IN_CONV conv%} fails if applied to a term that is not of the form {\small\verb%"t IN
+{t1,...,tn}"%}.  A call {\small\verb%IN_CONV conv "t IN {t1,...,tn}"%} fails unless the
+term {\small\verb%t%} is alpha-equivalent to some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
+{\small\verb%|- (t = ti) = T%} for some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
+{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}.
+
+\ENDDOC
+
 \DOC{INSERT\_CONV}
 
 \TYPE {\small\verb%INSERT_CONV : conv -> conv%}\egroup
@@ -257,84 +332,6 @@
 
 \ENDDOC
 
-\DOC{IN\_CONV}
-
-\TYPE {\small\verb%IN_CONV : conv -> conv%}\egroup
-
-\SYNOPSIS
-Decision procedure for membership in finite sets.
-
-\DESCRIBE 
-The function {\small\verb%IN_CONV%} is a parameterized conversion for proving or disproving
-membership assertions of the general form:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   "t IN {t1,...,tn}"
-\end{verbatim}
-}
-\noindent where {\small\verb%{t1,...,tn}%} is a set of type {\small\verb%(ty)set%} and {\small\verb%t%} is a value
-of the base type {\small\verb%ty%}.  The first argument to {\small\verb%IN_CONV%} is expected to be a
-conversion that decides equality between values of the base type {\small\verb%ty%}.  Given
-an equation {\small\verb%"e1 = e2"%}, where {\small\verb%e1%} and {\small\verb%e2%} are terms of type {\small\verb%ty%}, this
-conversion should return the theorem {\small\verb%|- (e1 = e2) = T%} or the theorem
-{\small\verb%|- (e1 = e2) = F%}, as appropriate.
-
-Given such a conversion, the function {\small\verb%IN_CONV%} returns a conversion that
-maps a term of the form {\small\verb%"t IN {t1,...,tn}"%} to the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- t IN {t1,...,tn} = T
-\end{verbatim}
-}
-
-\noindent if {\small\verb%t%} is alpha-equivalent to any {\small\verb%ti%}, or if the supplied conversion
-proves {\small\verb%|- (t = ti) = T%} for any {\small\verb%ti%}. If the supplied conversion proves
-{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}, then the result is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- t IN {t1,...,tn} = F 
-\end{verbatim}
-}
-\noindent In all other cases, {\small\verb%IN_CONV%} will fail.
-
-\EXAMPLE
-In the following example, the conversion {\small\verb%num_EQ_CONV%} is supplied as a
-parameter and used to test equality of the candidate element {\small\verb%1%} with the
-actual elements of the given set.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV num_EQ_CONV "2 IN {0,SUC 1,3}";;
-   |- 2 IN {0,SUC 1,3} = T
-\end{verbatim}
-}
-\noindent The result is {\small\verb%T%} because {\small\verb%num_EQ_CONV%} is able to prove that {\small\verb%2%} is
-equal to {\small\verb%SUC 1%}. An example of a negative result is:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV num_EQ_CONV "1 IN {0,2,3}";;
-   |- 1 IN {0,2,3} = F
-\end{verbatim}
-}
-\noindent Finally the behaviour of the supplied conversion is irrelevant when
-the value to be tested for membership is alpha-equivalent to an actual element:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV NO_CONV "1 IN {3,2,1}";;
-   |- 1 IN {3,2,1} = T
-\end{verbatim}
-}
-\noindent The conversion {\small\verb%NO_CONV%} always fails, but {\small\verb%IN_CONV%} is nontheless
-able in this case to prove the required result.
-
-\FAILURE
-{\small\verb%IN_CONV conv%} fails if applied to a term that is not of the form {\small\verb%"t IN
-{t1,...,tn}"%}.  A call {\small\verb%IN_CONV conv "t IN {t1,...,tn}"%} fails unless the
-term {\small\verb%t%} is alpha-equivalent to some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
-{\small\verb%|- (t = ti) = T%} for some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
-{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}.
-
-\ENDDOC
-
 \DOC{SET\_INDUCT\_TAC}
 
 \TYPE {\small\verb%SET_INDUCT_TAC : tactic%}\egroup
--- hol88-2.02.19940316.orig/Library/finite_sets/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/finite_sets/Manual/theorems.tex
@@ -1,7 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{The type definition}
-\THEOREM FINITE\_SET\_DEF finite\_sets
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{The type definition}\THEOREM FINITE\_SET\_DEF finite\_sets
 |- (!x. ~x IN {}) /\
    (!x y s. x IN (y INSERT s) = (x = y) \/ x IN s) /\
    (!x s. x INSERT (x INSERT s) = x INSERT s) /\
@@ -18,8 +15,7 @@
 \THEOREM set\_TY\_DEF finite\_sets
 |- ?rep. TYPE_DEFINITION IS_SET_REP rep
 \ENDTHEOREM
-\section{Basic properties of {\tt EMPTY}, {\tt INSERT}, and {\tt IN}}
-\THEOREM ABSORPTION finite\_sets
+\section{Basic properties of {\tt EMPTY}, {\tt INSERT}, and {\tt IN}}\THEOREM ABSORPTION finite\_sets
 |- !x s. x IN s = (x INSERT s = s)
 \ENDTHEOREM
 \THEOREM COMPONENT finite\_sets
@@ -31,15 +27,15 @@
 \THEOREM EXTENSION finite\_sets
 |- !s t. (s = t) = (!x. x IN s = x IN t)
 \ENDTHEOREM
+\THEOREM IN\_INSERT finite\_sets
+|- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
+\ENDTHEOREM
 \THEOREM INSERT\_COMM finite\_sets
 |- !x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)
 \ENDTHEOREM
 \THEOREM INSERT\_INSERT finite\_sets
 |- !x s. x INSERT (x INSERT s) = x INSERT s
 \ENDTHEOREM
-\THEOREM IN\_INSERT finite\_sets
-|- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
-\ENDTHEOREM
 \THEOREM MEMBER\_NOT\_EMPTY finite\_sets
 |- !s. (?x. x IN s) = ~(s = {})
 \ENDTHEOREM
@@ -49,12 +45,12 @@
 \THEOREM NOT\_EQUAL\_SETS finite\_sets
 |- !s t. ~(s = t) = (?x. x IN t = ~x IN s)
 \ENDTHEOREM
-\THEOREM NOT\_INSERT\_EMPTY finite\_sets
-|- !x s. ~(x INSERT s = {})
-\ENDTHEOREM
 \THEOREM NOT\_IN\_EMPTY finite\_sets
 |- !x. ~x IN {}
 \ENDTHEOREM
+\THEOREM NOT\_INSERT\_EMPTY finite\_sets
+|- !x s. ~(x INSERT s = {})
+\ENDTHEOREM
 \THEOREM NUM\_SET\_WOP finite\_sets
 |- !s. (?n. n IN s) = (?n. n IN s /\ (!m. m IN s ==> n <= m))
 \ENDTHEOREM
@@ -68,8 +64,7 @@
 \THEOREM SET\_MINIMUM finite\_sets
 |- !s M. (?x. x IN s) = (?x. x IN s /\ (!y. y IN s ==> (M x) <= (M y)))
 \ENDTHEOREM
-\section{Set inclusion}
-\THEOREM EMPTY\_SUBSET finite\_sets
+\section{Set inclusion}\THEOREM EMPTY\_SUBSET finite\_sets
 |- !s. {} SUBSET s
 \ENDTHEOREM
 \THEOREM INSERT\_SUBSET finite\_sets
@@ -111,13 +106,15 @@
 \THEOREM SUBSET\_TRANS finite\_sets
 |- !s t u. s SUBSET t /\ t SUBSET u ==> s SUBSET u
 \ENDTHEOREM
-\section{Intersection and union}
-\THEOREM DELETE\_INTER finite\_sets
+\section{Intersection and union}\THEOREM DELETE\_INTER finite\_sets
 |- !s t x. (s DELETE x) INTER t = (s INTER t) DELETE x
 \ENDTHEOREM
 \THEOREM EMPTY\_UNION finite\_sets
 |- !s t. (s UNION t = {}) = (s = {}) /\ (t = {})
 \ENDTHEOREM
+\THEOREM IN\_INTER finite\_sets
+|- !s t x. x IN (s INTER t) = x IN s /\ x IN t
+\ENDTHEOREM
 \THEOREM INSERT\_INTER finite\_sets
 |- !x s t.
     (x INSERT s) INTER t = (x IN t => x INSERT (s INTER t) | s INTER t)
@@ -147,21 +144,18 @@
 \THEOREM INTER\_SUBSET finite\_sets
 |- (!s t. (s INTER t) SUBSET s) /\ (!s t. (t INTER s) SUBSET s)
 \ENDTHEOREM
-\THEOREM IN\_INTER finite\_sets
-|- !s t x. x IN (s INTER t) = x IN s /\ x IN t
-\ENDTHEOREM
 \THEOREM IN\_UNION finite\_sets
 |- !s t x. x IN (s UNION t) = x IN s \/ x IN t
 \ENDTHEOREM
 \THEOREM SUBSET\_INTER\_ABSORPTION finite\_sets
 |- !s t. s SUBSET t = (s INTER t = s)
 \ENDTHEOREM
-\THEOREM SUBSET\_UNION finite\_sets
-|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
-\ENDTHEOREM
 \THEOREM SUBSET\_UNION\_ABSORPTION finite\_sets
 |- !s t. s SUBSET t = (s UNION t = t)
 \ENDTHEOREM
+\THEOREM SUBSET\_UNION finite\_sets
+|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
+\ENDTHEOREM
 \THEOREM UNION\_ASSOC finite\_sets
 |- !s t u. (s UNION t) UNION u = s UNION (t UNION u)
 \ENDTHEOREM
@@ -177,8 +171,7 @@
 \THEOREM UNION\_OVER\_INTER finite\_sets
 |- !s t u. s INTER (t UNION u) = (s INTER t) UNION (s INTER u)
 \ENDTHEOREM
-\section{Set difference}
-\THEOREM DIFF\_DIFF finite\_sets
+\section{Set difference}\THEOREM DIFF\_DIFF finite\_sets
 |- !s t. (s DIFF t) DIFF t = s DIFF t
 \ENDTHEOREM
 \THEOREM DIFF\_EMPTY finite\_sets
@@ -193,8 +186,7 @@
 \THEOREM IN\_DIFF finite\_sets
 |- !s t x. x IN (s DIFF t) = x IN s /\ ~x IN t
 \ENDTHEOREM
-\section{Deletion of an element}
-\THEOREM DELETE\_COMM finite\_sets
+\section{Deletion of an element}\THEOREM DELETE\_COMM finite\_sets
 |- !x y s. (s DELETE x) DELETE y = (s DELETE y) DELETE x
 \ENDTHEOREM
 \THEOREM DELETE\_DEF finite\_sets
@@ -220,9 +212,6 @@
 \THEOREM EMPTY\_DELETE finite\_sets
 |- !x. {} DELETE x = {}
 \ENDTHEOREM
-\THEOREM INSERT\_DELETE finite\_sets
-|- !x s. x IN s ==> (x INSERT (s DELETE x) = s)
-\ENDTHEOREM
 \THEOREM IN\_DELETE finite\_sets
 |- !s x y. x IN (s DELETE y) = x IN s /\ ~(x = y)
 \ENDTHEOREM
@@ -230,14 +219,16 @@
 |- !s x x'.
     (x IN s = x' IN s) = (x IN (s DELETE x') = x' IN (s DELETE x))
 \ENDTHEOREM
+\THEOREM INSERT\_DELETE finite\_sets
+|- !x s. x IN s ==> (x INSERT (s DELETE x) = s)
+\ENDTHEOREM
 \THEOREM SUBSET\_DELETE finite\_sets
 |- !x s t. s SUBSET (t DELETE x) = ~x IN s /\ s SUBSET t
 \ENDTHEOREM
 \THEOREM SUBSET\_INSERT\_DELETE finite\_sets
 |- !x s t. s SUBSET (x INSERT t) = (s DELETE x) SUBSET t
 \ENDTHEOREM
-\section{Disjoint sets}
-\THEOREM DISJOINT\_DEF finite\_sets
+\section{Disjoint sets}\THEOREM DISJOINT\_DEF finite\_sets
 |- !s t. DISJOINT s t = (s INTER t = {})
 \ENDTHEOREM
 \THEOREM DISJOINT\_DELETE\_SYM finite\_sets
@@ -261,8 +252,7 @@
 \THEOREM IN\_DISJOINT finite\_sets
 |- !s t. DISJOINT s t = ~(?x. x IN s /\ x IN t)
 \ENDTHEOREM
-\section{The {\tt CHOICE} and {\tt REST} functions}
-\THEOREM CHOICE\_DEF finite\_sets
+\section{The {\tt CHOICE} and {\tt REST} functions}\THEOREM CHOICE\_DEF finite\_sets
 |- !s. ~(s = {}) ==> (CHOICE s) IN s
 \ENDTHEOREM
 \THEOREM CHOICE\_INSERT\_REST finite\_sets
@@ -289,8 +279,7 @@
 \THEOREM SING\_IFF\_EMPTY\_REST finite\_sets
 |- !s. SING s = ~(s = {}) /\ (REST s = {})
 \ENDTHEOREM
-\section{Image of a function on a set}
-\THEOREM IMAGE\_COMPOSE finite\_sets
+\section{Image of a function on a set}\THEOREM IMAGE\_COMPOSE finite\_sets
 |- !f g s. IMAGE(f o g)s = IMAGE f(IMAGE g s)
 \ENDTHEOREM
 \THEOREM IMAGE\_DELETE finite\_sets
@@ -323,8 +312,7 @@
 \THEOREM IN\_IMAGE finite\_sets
 |- !f s y. y IN (IMAGE f s) = (?x. (y = f x) /\ x IN s)
 \ENDTHEOREM
-\section{Mappings between sets}
-\THEOREM BIJ\_COMPOSE finite\_sets
+\section{Mappings between sets}\THEOREM BIJ\_COMPOSE finite\_sets
 |- !f g s t u. BIJ f s t /\ BIJ g t u ==> BIJ(g o f)s u
 \ENDTHEOREM
 \THEOREM BIJ\_DEF finite\_sets
@@ -375,8 +363,7 @@
 \THEOREM SURJ\_ID finite\_sets
 |- !s. SURJ(\x. x)s s
 \ENDTHEOREM
-\section{Singleton sets}
-\THEOREM DELETE\_EQ\_SING finite\_sets
+\section{Singleton sets}\THEOREM DELETE\_EQ\_SING finite\_sets
 |- !s x. x IN s ==> ((s DELETE x = {}) = (s = {x}))
 \ENDTHEOREM
 \THEOREM DISJOINT\_SING\_EMPTY finite\_sets
@@ -397,17 +384,16 @@
 \THEOREM NOT\_SING\_EMPTY finite\_sets
 |- !x. ~({x} = {})
 \ENDTHEOREM
-\THEOREM SING finite\_sets
-|- !x. SING{x}
-\ENDTHEOREM
 \THEOREM SING\_DEF finite\_sets
 |- !s. SING s = (?x. s = {x})
 \ENDTHEOREM
 \THEOREM SING\_DELETE finite\_sets
 |- !x. {x} DELETE x = {}
 \ENDTHEOREM
-\section{Cardinality of sets}
-\THEOREM CARD\_DEF finite\_sets
+\THEOREM SING finite\_sets
+|- !x. SING{x}
+\ENDTHEOREM
+\section{Cardinality of sets}\THEOREM CARD\_DEF finite\_sets
 |- (CARD{} = 0) /\
    (!s x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s)))
 \ENDTHEOREM
--- hol88-2.02.19940316.orig/Library/window/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/window/Manual/theorems.tex
@@ -1,11 +1,7 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{Definitions}
-\THEOREM PMI\_DEF win
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{Definitions}\THEOREM PMI\_DEF win
 |- !a b. a <== b = b ==> a
 \ENDTHEOREM
-\section{Theorems}
-\THEOREM IMP\_REFL\_THM win
+\section{Theorems}\THEOREM IMP\_REFL\_THM win
 |- !x. x ==> x
 \ENDTHEOREM
 \THEOREM IMP\_TRANS\_THM win
--- hol88-2.02.19940316.orig/Library/word/Manual/entries.tex
+++ hol88-2.02.19940316/Library/word/Manual/entries.tex
@@ -1,7 +1,4 @@
-\chapter{ML Functions in the {\tt word} Library}
-\label{entries}
-\input{entries-intro}
-\DOC{BIT\_CONV}
+\chapter{ML Functions in the {\tt word} Library}\label{entries}\input{entries-intro}\DOC{BIT\_CONV}
 
 \TYPE {\small\verb%BIT_CONV : conv%}\egroup
 
--- hol88-2.02.19940316.orig/Library/word/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/word/Manual/theorems.tex
@@ -1,7 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{The theory {\tt word\_base}}
-\THEOREM BIT0 word\_base
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{The theory {\tt word\_base}}\THEOREM BIT0 word\_base
 |- !b. BIT 0(WORD[b]) = b
 \ENDTHEOREM
 \THEOREM BIT\_DEF word\_base
@@ -33,20 +30,17 @@
      !m k j.
       (m + k) <= n ==> j < m ==> (BIT j(WSEG m k w) = BIT(j + k)w)
 \ENDTHEOREM
-\THEOREM LSB word\_base
-|- !n. !w :: PWORDLEN n. 0 < n ==> (LSB w = BIT 0 w)
-\ENDTHEOREM
 \THEOREM LSB\_DEF word\_base
 |- !l. LSB(WORD l) = LAST l
 \ENDTHEOREM
-\THEOREM MSB word\_base
-|- !n. !w :: PWORDLEN n. 0 < n ==> (MSB w = BIT(PRE n)w)
+\THEOREM LSB word\_base
+|- !n. !w :: PWORDLEN n. 0 < n ==> (LSB w = BIT 0 w)
 \ENDTHEOREM
 \THEOREM MSB\_DEF word\_base
 |- !l. MSB(WORD l) = HD l
 \ENDTHEOREM
-\THEOREM PWORDLEN word\_base
-|- !n w. PWORDLEN n w = (WORDLEN w = n)
+\THEOREM MSB word\_base
+|- !n. !w :: PWORDLEN n. 0 < n ==> (MSB w = BIT(PRE n)w)
 \ENDTHEOREM
 \THEOREM PWORDLEN0 word\_base
 |- !w. PWORDLEN 0 w ==> (w = WORD[])
@@ -57,6 +51,9 @@
 \THEOREM PWORDLEN\_DEF word\_base
 |- !n l. PWORDLEN n(WORD l) = (n = LENGTH l)
 \ENDTHEOREM
+\THEOREM PWORDLEN word\_base
+|- !n w. PWORDLEN n w = (WORDLEN w = n)
+\ENDTHEOREM
 \THEOREM WCAT0 word\_base
 |- !w. (WCAT(WORD[],w) = w) /\ (WCAT(w,WORD[]) = w)
 \ENDTHEOREM
@@ -84,26 +81,6 @@
       (m1 + (m2 + k)) <= n ==>
       (WCAT(WSEG m2(m1 + k)w,WSEG m1 k w) = WSEG(m1 + m2)k w)
 \ENDTHEOREM
-\THEOREM WORDLEN\_DEF word\_base
-|- !l. WORDLEN(WORD l) = LENGTH l
-\ENDTHEOREM
-\THEOREM WORDLEN\_SUC\_WCAT word\_base
-|- !n w.
-    PWORDLEN(SUC n)w ==>
-    (?b :: PWORDLEN 1. ?w' :: PWORDLEN n. w = WCAT(b,w'))
-\ENDTHEOREM
-\THEOREM WORDLEN\_SUC\_WCAT\_BIT\_WSEG word\_base
-|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WORD[BIT n w],WSEG n 0 w)
-\ENDTHEOREM
-\THEOREM WORDLEN\_SUC\_WCAT\_BIT\_WSEG\_RIGHT word\_base
-|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WORD[BIT 0 w])
-\ENDTHEOREM
-\THEOREM WORDLEN\_SUC\_WCAT\_WSEG\_WSEG word\_base
-|- !w :: PWORDLEN(SUC n). w = WCAT(WSEG 1 n w,WSEG n 0 w)
-\ENDTHEOREM
-\THEOREM WORDLEN\_SUC\_WCAT\_WSEG\_WSEG\_RIGHT word\_base
-|- !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WSEG 1 0 w)
-\ENDTHEOREM
 \THEOREM WORD\_11 word\_base
 |- !l l'. (WORD l = WORD l') = (l = l')
 \ENDTHEOREM
@@ -128,6 +105,26 @@
      TRP(\v tl. (?l. v = l) /\ (LENGTH tl = 0))r =
      (REP_word(ABS_word r) = r))
 \ENDTHEOREM
+\THEOREM WORDLEN\_DEF word\_base
+|- !l. WORDLEN(WORD l) = LENGTH l
+\ENDTHEOREM
+\THEOREM WORDLEN\_SUC\_WCAT\_BIT\_WSEG word\_base
+|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WORD[BIT n w],WSEG n 0 w)
+\ENDTHEOREM
+\THEOREM WORDLEN\_SUC\_WCAT\_BIT\_WSEG\_RIGHT word\_base
+|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WORD[BIT 0 w])
+\ENDTHEOREM
+\THEOREM WORDLEN\_SUC\_WCAT word\_base
+|- !n w.
+    PWORDLEN(SUC n)w ==>
+    (?b :: PWORDLEN 1. ?w' :: PWORDLEN n. w = WCAT(b,w'))
+\ENDTHEOREM
+\THEOREM WORDLEN\_SUC\_WCAT\_WSEG\_WSEG word\_base
+|- !w :: PWORDLEN(SUC n). w = WCAT(WSEG 1 n w,WSEG n 0 w)
+\ENDTHEOREM
+\THEOREM WORDLEN\_SUC\_WCAT\_WSEG\_WSEG\_RIGHT word\_base
+|- !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WSEG 1 0 w)
+\ENDTHEOREM
 \THEOREM WORD\_PARTITION word\_base
 |- (!n. !w :: PWORDLEN n. !m. m <= n ==> (WCAT(WSPLIT m w) = w)) /\
    (!n m.
@@ -162,15 +159,6 @@
 |- !n1 n2.
     !w1 :: PWORDLEN n1. !w2 :: PWORDLEN n2. WSEG n2 0(WCAT(w1,w2)) = w2
 \ENDTHEOREM
-\THEOREM WSEG\_WCAT\_WSEG word\_base
-|- !n1 n2.
-    !w1 :: PWORDLEN n1.
-     !w2 :: PWORDLEN n2.
-      !m k.
-       (m + k) <= (n1 + n2) /\ k < n2 /\ n2 <= (m + k) ==>
-       (WSEG m k(WCAT(w1,w2)) =
-        WCAT(WSEG((m + k) - n2)0 w1,WSEG(n2 - k)k w2))
-\ENDTHEOREM
 \THEOREM WSEG\_WCAT\_WSEG1 word\_base
 |- !n1 n2.
     !w1 :: PWORDLEN n1.
@@ -184,6 +172,15 @@
      !w2 :: PWORDLEN n2.
       !m k. (m + k) <= n2 ==> (WSEG m k(WCAT(w1,w2)) = WSEG m k w2)
 \ENDTHEOREM
+\THEOREM WSEG\_WCAT\_WSEG word\_base
+|- !n1 n2.
+    !w1 :: PWORDLEN n1.
+     !w2 :: PWORDLEN n2.
+      !m k.
+       (m + k) <= (n1 + n2) /\ k < n2 /\ n2 <= (m + k) ==>
+       (WSEG m k(WCAT(w1,w2)) =
+        WCAT(WSEG((m + k) - n2)0 w1,WSEG(n2 - k)k w2))
+\ENDTHEOREM
 \THEOREM WSEG\_WORDLEN word\_base
 |- !n.
     !w :: PWORDLEN n. !m k. (m + k) <= n ==> (WORDLEN(WSEG m k w) = m)
@@ -208,11 +205,6 @@
       m <= n ==>
       PWORDLEN(n - m)(FST(WSPLIT m w)) /\ PWORDLEN m(SND(WSPLIT m w))
 \ENDTHEOREM
-\THEOREM WSPLIT\_WSEG word\_base
-|- !n.
-    !w :: PWORDLEN n.
-     !k. k <= n ==> (WSPLIT k w = WSEG(n - k)k w,WSEG k 0 w)
-\ENDTHEOREM
 \THEOREM WSPLIT\_WSEG1 word\_base
 |- !n.
     !w :: PWORDLEN n. !k. k <= n ==> (FST(WSPLIT k w) = WSEG(n - k)k w)
@@ -220,13 +212,17 @@
 \THEOREM WSPLIT\_WSEG2 word\_base
 |- !n. !w :: PWORDLEN n. !k. k <= n ==> (SND(WSPLIT k w) = WSEG k 0 w)
 \ENDTHEOREM
-\section{The theory {\tt word\_bitop}}
-\THEOREM EXISTSABIT word\_bitop
-|- !n. !w :: PWORDLEN n. !P. EXISTSABIT P w = (?k. k < n /\ P(BIT k w))
+\THEOREM WSPLIT\_WSEG word\_base
+|- !n.
+    !w :: PWORDLEN n.
+     !k. k <= n ==> (WSPLIT k w = WSEG(n - k)k w,WSEG k 0 w)
 \ENDTHEOREM
-\THEOREM EXISTSABIT\_DEF word\_bitop
+\section{The theory {\tt word\_bitop}}\THEOREM EXISTSABIT\_DEF word\_bitop
 |- !P l. EXISTSABIT P(WORD l) = SOME_EL P l
 \ENDTHEOREM
+\THEOREM EXISTSABIT word\_bitop
+|- !n. !w :: PWORDLEN n. !P. EXISTSABIT P w = (?k. k < n /\ P(BIT k w))
+\ENDTHEOREM
 \THEOREM EXISTSABIT\_WCAT word\_bitop
 |- !w1 w2 P.
     EXISTSABIT P(WCAT(w1,w2)) = EXISTSABIT P w1 \/ EXISTSABIT P w2
@@ -237,12 +233,12 @@
      !m k.
       (m + k) <= n ==> (!P. EXISTSABIT P(WSEG m k w) ==> EXISTSABIT P w)
 \ENDTHEOREM
-\THEOREM FORALLBITS word\_bitop
-|- !n. !w :: PWORDLEN n. !P. FORALLBITS P w = (!k. k < n ==> P(BIT k w))
-\ENDTHEOREM
 \THEOREM FORALLBITS\_DEF word\_bitop
 |- !P l. FORALLBITS P(WORD l) = ALL_EL P l
 \ENDTHEOREM
+\THEOREM FORALLBITS word\_bitop
+|- !n. !w :: PWORDLEN n. !P. FORALLBITS P w = (!k. k < n ==> P(BIT k w))
+\ENDTHEOREM
 \THEOREM FORALLBITS\_WCAT word\_bitop
 |- !w1 w2 P.
     FORALLBITS P(WCAT(w1,w2)) = FORALLBITS P w1 /\ FORALLBITS P w2
@@ -316,6 +312,16 @@
     BIT(PRE(WORDLEN w))w,
     WCAT(WSEG(PRE(WORDLEN w))0 w,(f => WSEG 1 0 w | WORD[b]))
 \ENDTHEOREM
+\THEOREM SHL\_WSEG\_1F word\_bitop
+|- !n.
+    !w :: PWORDLEN n.
+     !m k.
+      (m + k) <= n ==>
+      0 < m ==>
+      (!b.
+        SHL F(WSEG m k w)b =
+        BIT(k + (m - 1))w,WCAT(WSEG(m - 1)k w,WORD[b]))
+\ENDTHEOREM
 \THEOREM SHL\_WSEG word\_bitop
 |- !n.
     !w :: PWORDLEN n.
@@ -329,16 +335,6 @@
          WCAT(WSEG(m - 1)k w,WSEG 1 k w) | 
          WCAT(WSEG(m - 1)k w,WORD[b])))
 \ENDTHEOREM
-\THEOREM SHL\_WSEG\_1F word\_bitop
-|- !n.
-    !w :: PWORDLEN n.
-     !m k.
-      (m + k) <= n ==>
-      0 < m ==>
-      (!b.
-        SHL F(WSEG m k w)b =
-        BIT(k + (m - 1))w,WCAT(WSEG(m - 1)k w,WORD[b]))
-\ENDTHEOREM
 \THEOREM SHL\_WSEG\_NF word\_bitop
 |- !n.
     !w :: PWORDLEN n.
@@ -356,26 +352,26 @@
     ((f => WSEG 1(PRE(WORDLEN w))w | WORD[b]),WSEG(PRE(WORDLEN w))1 w),
     BIT 0 w
 \ENDTHEOREM
-\THEOREM SHR\_WSEG word\_bitop
+\THEOREM SHR\_WSEG\_1F word\_bitop
 |- !n.
     !w :: PWORDLEN n.
      !m k.
       (m + k) <= n ==>
       0 < m ==>
-      (!f b.
-        SHR f b(WSEG m k w) =
-        (f => 
-         WCAT(WSEG 1(k + (m - 1))w,WSEG(m - 1)(k + 1)w) | 
-         WCAT(WORD[b],WSEG(m - 1)(k + 1)w)),BIT k w)
+      (!b.
+        SHR F b(WSEG m k w) = WCAT(WORD[b],WSEG(m - 1)(k + 1)w),BIT k w)
 \ENDTHEOREM
-\THEOREM SHR\_WSEG\_1F word\_bitop
+\THEOREM SHR\_WSEG word\_bitop
 |- !n.
     !w :: PWORDLEN n.
      !m k.
       (m + k) <= n ==>
       0 < m ==>
-      (!b.
-        SHR F b(WSEG m k w) = WCAT(WORD[b],WSEG(m - 1)(k + 1)w),BIT k w)
+      (!f b.
+        SHR f b(WSEG m k w) =
+        (f => 
+         WCAT(WSEG 1(k + (m - 1))w,WSEG(m - 1)(k + 1)w) | 
+         WCAT(WORD[b],WSEG(m - 1)(k + 1)w)),BIT k w)
 \ENDTHEOREM
 \THEOREM SHR\_WSEG\_NF word\_bitop
 |- !n.
@@ -413,13 +409,6 @@
      !m k.
       (m + k) <= n ==> (!f. WMAP f(WSEG m k w) = WSEG m k(WMAP f w))
 \ENDTHEOREM
-\THEOREM WSEG\_SHL word\_bitop
-|- !n.
-    !w :: PWORDLEN(SUC n).
-     !m k.
-      0 < k /\ (m + k) <= (SUC n) ==>
-      (!b. WSEG m k(SND(SHL f w b)) = WSEG m(k - 1)w)
-\ENDTHEOREM
 \THEOREM WSEG\_SHL\_0 word\_bitop
 |- !n.
     !w :: PWORDLEN(SUC n).
@@ -428,15 +417,21 @@
       (WSEG m 0(SND(SHL f w b)) =
        WCAT(WSEG(m - 1)0 w,(f => WSEG 1 0 w | WORD[b])))
 \ENDTHEOREM
-\section{The theory {\tt word\_num}}
+\THEOREM WSEG\_SHL word\_bitop
+|- !n.
+    !w :: PWORDLEN(SUC n).
+     !m k.
+      0 < k /\ (m + k) <= (SUC n) ==>
+      (!b. WSEG m k(SND(SHL f w b)) = WSEG m(k - 1)w)
+\ENDTHEOREM
+\section{The theory {\tt word\_num}}\THEOREM LVAL\_DEF word\_num
+|- !f b l. LVAL f b l = FOLDL(\e x. (b * e) + (f x))0 l
+\ENDTHEOREM
 \THEOREM LVAL word\_num
 |- (!f b. LVAL f b[] = 0) /\
    (!l f b x.
      LVAL f b(CONS x l) = ((f x) * (b EXP (LENGTH l))) + (LVAL f b l))
 \ENDTHEOREM
-\THEOREM LVAL\_DEF word\_num
-|- !f b l. LVAL f b l = FOLDL(\e x. (b * e) + (f x))0 l
-\ENDTHEOREM
 \THEOREM LVAL\_MAX word\_num
 |- !l f b. (!x. (f x) < b) ==> (LVAL f b l) < (b EXP (LENGTH l))
 \ENDTHEOREM
@@ -461,14 +456,6 @@
 |- !f b.
     (!x. (f x) < b) ==> (!n. !w :: PWORDLEN n. (NVAL f b w) < (b EXP n))
 \ENDTHEOREM
-\THEOREM NVAL\_WCAT word\_num
-|- !n m.
-    !w1 :: PWORDLEN n.
-     !w2 :: PWORDLEN m.
-      !f b.
-       NVAL f b(WCAT(w1,w2)) =
-       ((NVAL f b w1) * (b EXP m)) + (NVAL f b w2)
-\ENDTHEOREM
 \THEOREM NVAL\_WCAT1 word\_num
 |- !w f b x. NVAL f b(WCAT(w,WORD[x])) = ((NVAL f b w) * b) + (f x)
 \ENDTHEOREM
@@ -478,6 +465,14 @@
      !f b x.
       NVAL f b(WCAT(WORD[x],w)) = ((f x) * (b EXP n)) + (NVAL f b w)
 \ENDTHEOREM
+\THEOREM NVAL\_WCAT word\_num
+|- !n m.
+    !w1 :: PWORDLEN n.
+     !w2 :: PWORDLEN m.
+      !f b.
+       NVAL f b(WCAT(w1,w2)) =
+       ((NVAL f b w1) * (b EXP m)) + (NVAL f b w2)
+\ENDTHEOREM
 \THEOREM NVAL\_WORDLEN\_0 word\_num
 |- !w :: PWORDLEN 0. !fv r. NVAL fv r w = 0
 \ENDTHEOREM
@@ -490,8 +485,7 @@
 \THEOREM NWORD\_PWORDLEN word\_num
 |- !n f b m. PWORDLEN n(NWORD n f b m)
 \ENDTHEOREM
-\section{The theory {\tt bword\_bitop}}
-\THEOREM PBITBOP\_WAND bword\_bitop
+\section{The theory {\tt bword\_bitop}}\THEOREM PBITBOP\_WAND bword\_bitop
 |- PBITBOP $WAND
 \ENDTHEOREM
 \THEOREM PBITBOP\_WOR bword\_bitop
@@ -523,8 +517,7 @@
 \THEOREM WXOR\_DEF bword\_bitop
 |- !l1 l2. (WORD l1) WXOR (WORD l2) = WORD(MAP2(\x y. ~(x = y))l1 l2)
 \ENDTHEOREM
-\section{The theory {\tt bword\_num}}
-\THEOREM ADD\_BNVAL\_LEFT bword\_num
+\section{The theory {\tt bword\_num}}\THEOREM ADD\_BNVAL\_LEFT bword\_num
 |- !n.
     !w1 w2 :: PWORDLEN(SUC n).
      (BNVAL w1) + (BNVAL w2) =
@@ -570,12 +563,6 @@
 \THEOREM BNVAL\_ONTO bword\_num
 |- !w. ?n. BNVAL w = n
 \ENDTHEOREM
-\THEOREM BNVAL\_WCAT bword\_num
-|- !n m.
-    !w1 :: PWORDLEN n.
-     !w2 :: PWORDLEN m.
-      BNVAL(WCAT(w1,w2)) = ((BNVAL w1) * (2 EXP m)) + (BNVAL w2)
-\ENDTHEOREM
 \THEOREM BNVAL\_WCAT1 bword\_num
 |- !n.
     !w :: PWORDLEN n.
@@ -586,6 +573,12 @@
     !w :: PWORDLEN n.
      !x. BNVAL(WCAT(WORD[x],w)) = ((BV x) * (2 EXP n)) + (BNVAL w)
 \ENDTHEOREM
+\THEOREM BNVAL\_WCAT bword\_num
+|- !n m.
+    !w1 :: PWORDLEN n.
+     !w2 :: PWORDLEN m.
+      BNVAL(WCAT(w1,w2)) = ((BNVAL w1) * (2 EXP m)) + (BNVAL w2)
+\ENDTHEOREM
 \THEOREM BV\_DEF bword\_num
 |- !b. BV b = (b => SUC 0 | 0)
 \ENDTHEOREM
@@ -667,8 +660,7 @@
 \THEOREM ZERO\_WORD\_VAL bword\_num
 |- !n. !w :: PWORDLEN n. (w = NBWORD n 0) = (BNVAL w = 0)
 \ENDTHEOREM
-\section{The theory {\tt bword\_arith}}
-\THEOREM ACARRY\_ACARRY\_WSEG bword\_arith
+\section{The theory {\tt bword\_arith}}\THEOREM ACARRY\_ACARRY\_WSEG bword\_arith
 |- !n.
     !w1 w2 :: PWORDLEN n.
      !cin m k1 k2.
--- hol88-2.02.19940316.orig/Library/numeral/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/numeral/Manual/theorems.tex
@@ -1,13 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{Numeral theory}
-\THEOREM BASEN numeral
-|- (!radix. BASEN radix[] = 0) /\
-   (!radix digit digits.
-     BASEN radix(CONS digit digits) =
-     (digit * (radix EXP (LENGTH digits))) + (BASEN radix digits))
-\ENDTHEOREM
-\THEOREM BASEN\_11 numeral
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{Numeral theory}\THEOREM BASEN\_11 numeral
 |- !r l1 l2.
     1 < r ==>
     IS_BASEN r l1 ==>
@@ -24,14 +15,20 @@
 \THEOREM BASEN\_CONS\_0 numeral
 |- !r l. BASEN r(CONS 0 l) = BASEN r l
 \ENDTHEOREM
+\THEOREM BASEN\_DIGIT\_EQ\_DIGIT numeral
+|- !r e. BASEN r[e] = e
+\ENDTHEOREM
 \THEOREM BASEN\_DIGITS numeral
 |- !n m r.
     1 < r ==>
     (LENGTH(BASEN_DIGITS r n m) = n) /\
     (BASEN r(BASEN_DIGITS r n m) = m MOD (r EXP n))
 \ENDTHEOREM
-\THEOREM BASEN\_DIGIT\_EQ\_DIGIT numeral
-|- !r e. BASEN r[e] = e
+\THEOREM BASEN numeral
+|- (!radix. BASEN radix[] = 0) /\
+   (!radix digit digits.
+     BASEN radix(CONS digit digits) =
+     (digit * (radix EXP (LENGTH digits))) + (BASEN radix digits))
 \ENDTHEOREM
 \THEOREM BASEN\_EMPTY\_EQ\_0 numeral
 |- !r l. 1 < r ==> IS_NORMALIZED l ==> ((BASEN r l = 0) = (l = []))
@@ -85,9 +82,6 @@
 \THEOREM BASEN\_ZEROS numeral
 |- !r n. BASEN r(REPLICATE n 0) = 0
 \ENDTHEOREM
-\THEOREM BINARY numeral
-|- BINARY = BASEN 2
-\ENDTHEOREM
 \THEOREM BINARY\_11 numeral
 |- !l1 l2.
     IS_BINARY l1 ==>
@@ -102,6 +96,9 @@
 \THEOREM BINARY\_DIGIT\_EQ\_DIGIT numeral
 |- !e. BINARY[e] = e
 \ENDTHEOREM
+\THEOREM BINARY numeral
+|- BINARY = BASEN 2
+\ENDTHEOREM
 \THEOREM BINARY\_EMPTY\_EQ\_0 numeral
 |- !l. IS_NORMALIZED l ==> ((BINARY l = 0) = (l = []))
 \ENDTHEOREM
@@ -134,9 +131,6 @@
 \THEOREM BINARY\_ZEROS numeral
 |- !n. BINARY(REPLICATE n 0) = 0
 \ENDTHEOREM
-\THEOREM DECIMAL numeral
-|- DECIMAL = BASEN 10
-\ENDTHEOREM
 \THEOREM DECIMAL\_11 numeral
 |- !l1 l2.
     IS_DECIMAL l1 ==>
@@ -151,6 +145,9 @@
 \THEOREM DECIMAL\_DIGIT\_EQ\_DIGIT numeral
 |- !e. DECIMAL[e] = e
 \ENDTHEOREM
+\THEOREM DECIMAL numeral
+|- DECIMAL = BASEN 10
+\ENDTHEOREM
 \THEOREM DECIMAL\_EMPTY\_EQ\_0 numeral
 |- !l. IS_NORMALIZED l ==> ((DECIMAL l = 0) = (l = []))
 \ENDTHEOREM
@@ -183,9 +180,6 @@
 \THEOREM DECIMAL\_ZEROS numeral
 |- !n. DECIMAL(REPLICATE n 0) = 0
 \ENDTHEOREM
-\THEOREM HEX numeral
-|- HEX = BASEN 16
-\ENDTHEOREM
 \THEOREM HEX\_11 numeral
 |- !l1 l2.
     IS_HEX l1 ==>
@@ -200,6 +194,9 @@
 \THEOREM HEX\_DIGIT\_EQ\_DIGIT numeral
 |- !e. HEX[e] = e
 \ENDTHEOREM
+\THEOREM HEX numeral
+|- HEX = BASEN 16
+\ENDTHEOREM
 \THEOREM HEX\_EMPTY\_EQ\_0 numeral
 |- !l. IS_NORMALIZED l ==> ((HEX l = 0) = (l = []))
 \ENDTHEOREM
@@ -232,9 +229,6 @@
 \THEOREM HEX\_ZEROS numeral
 |- !n. HEX(REPLICATE n 0) = 0
 \ENDTHEOREM
-\THEOREM IS\_BASEN numeral
-|- !radix digits. IS_BASEN radix digits = EVERY($> radix)digits
-\ENDTHEOREM
 \THEOREM IS\_BASEN\_APPEND numeral
 |- !r l m. IS_BASEN r(APPEND l m) = IS_BASEN r l /\ IS_BASEN r m
 \ENDTHEOREM
@@ -250,12 +244,12 @@
 \THEOREM IS\_BASEN\_CONS\_IMP\_LESS numeral
 |- !r l e. 1 < r ==> IS_BASEN r(CONS e l) ==> e < r
 \ENDTHEOREM
+\THEOREM IS\_BASEN numeral
+|- !radix digits. IS_BASEN radix digits = EVERY($> radix)digits
+\ENDTHEOREM
 \THEOREM IS\_BASEN\_NIL numeral
 |- !r. IS_BASEN r[]
 \ENDTHEOREM
-\THEOREM IS\_BINARY numeral
-|- IS_BINARY = IS_BASEN 2
-\ENDTHEOREM
 \THEOREM IS\_BINARY\_CONS numeral
 |- !l e. IS_BINARY(CONS e l) = e < 2 /\ IS_BINARY l
 \ENDTHEOREM
@@ -265,6 +259,9 @@
 \THEOREM IS\_BINARY\_CONS\_IMP\_LESS numeral
 |- !l e. IS_BINARY(CONS e l) ==> e < 2
 \ENDTHEOREM
+\THEOREM IS\_BINARY numeral
+|- IS_BINARY = IS_BASEN 2
+\ENDTHEOREM
 \THEOREM IS\_BINARY\_NIL numeral
 |- IS_BINARY[]
 \ENDTHEOREM
@@ -273,9 +270,6 @@
     IS_BINARY_NORMALIZED digits =
     IS_BINARY digits /\ IS_NORMALIZED digits
 \ENDTHEOREM
-\THEOREM IS\_DECIMAL numeral
-|- IS_DECIMAL = IS_BASEN 10
-\ENDTHEOREM
 \THEOREM IS\_DECIMAL\_CONS numeral
 |- !l e. IS_DECIMAL(CONS e l) = e < 10 /\ IS_DECIMAL l
 \ENDTHEOREM
@@ -285,6 +279,9 @@
 \THEOREM IS\_DECIMAL\_CONS\_IMP\_LESS numeral
 |- !l e. IS_DECIMAL(CONS e l) ==> e < 10
 \ENDTHEOREM
+\THEOREM IS\_DECIMAL numeral
+|- IS_DECIMAL = IS_BASEN 10
+\ENDTHEOREM
 \THEOREM IS\_DECIMAL\_NIL numeral
 |- IS_DECIMAL[]
 \ENDTHEOREM
@@ -293,9 +290,6 @@
     IS_DECIMAL_NORMALIZED digits =
     IS_DECIMAL digits /\ IS_NORMALIZED digits
 \ENDTHEOREM
-\THEOREM IS\_HEX numeral
-|- IS_HEX = IS_BASEN 16
-\ENDTHEOREM
 \THEOREM IS\_HEX\_CONS numeral
 |- !l e. IS_HEX(CONS e l) = e < 16 /\ IS_HEX l
 \ENDTHEOREM
@@ -305,6 +299,9 @@
 \THEOREM IS\_HEX\_CONS\_IMP\_LESS numeral
 |- !l e. IS_HEX(CONS e l) ==> e < 16
 \ENDTHEOREM
+\THEOREM IS\_HEX numeral
+|- IS_HEX = IS_BASEN 16
+\ENDTHEOREM
 \THEOREM IS\_HEX\_NIL numeral
 |- IS_HEX[]
 \ENDTHEOREM
@@ -312,18 +309,15 @@
 |- !digits.
     IS_HEX_NORMALIZED digits = IS_HEX digits /\ IS_NORMALIZED digits
 \ENDTHEOREM
-\THEOREM IS\_NORMALIZED numeral
-|- !digits. IS_NORMALIZED digits = (digits = []) \/ 0 < (HD digits)
-\ENDTHEOREM
 \THEOREM IS\_NORMALIZED\_CONS numeral
 |- !e l. IS_NORMALIZED(CONS e l) = 0 < e
 \ENDTHEOREM
+\THEOREM IS\_NORMALIZED numeral
+|- !digits. IS_NORMALIZED digits = (digits = []) \/ 0 < (HD digits)
+\ENDTHEOREM
 \THEOREM IS\_NORMALIZED\_NIL numeral
 |- IS_NORMALIZED[]
 \ENDTHEOREM
-\THEOREM IS\_OCTAL numeral
-|- IS_OCTAL = IS_BASEN 8
-\ENDTHEOREM
 \THEOREM IS\_OCTAL\_CONS numeral
 |- !l e. IS_OCTAL(CONS e l) = e < 8 /\ IS_OCTAL l
 \ENDTHEOREM
@@ -333,6 +327,9 @@
 \THEOREM IS\_OCTAL\_CONS\_IMP\_LESS numeral
 |- !l e. IS_OCTAL(CONS e l) ==> e < 8
 \ENDTHEOREM
+\THEOREM IS\_OCTAL numeral
+|- IS_OCTAL = IS_BASEN 8
+\ENDTHEOREM
 \THEOREM IS\_OCTAL\_NIL numeral
 |- IS_OCTAL[]
 \ENDTHEOREM
@@ -340,12 +337,12 @@
 |- !digits.
     IS_OCTAL_NORMALIZED digits = IS_OCTAL digits /\ IS_NORMALIZED digits
 \ENDTHEOREM
-\THEOREM LOG numeral
-|- !r n. LOG r n = (@x. (r EXP x) <= n /\ n < (r EXP (x + 1)))
-\ENDTHEOREM
 \THEOREM LOG\_1 numeral
 |- !r. 1 < r ==> (LOG r 1 = 0)
 \ENDTHEOREM
+\THEOREM LOG numeral
+|- !r n. LOG r n = (@x. (r EXP x) <= n /\ n < (r EXP (x + 1)))
+\ENDTHEOREM
 \THEOREM NORMALIZED\_BASEN\_11 numeral
 |- !l1 l2 r.
     1 < r ==>
@@ -376,9 +373,6 @@
       (BASEN r l1 = BASEN r l2) /\
       (LENGTH l1) < (LENGTH l2))
 \ENDTHEOREM
-\THEOREM OCTAL numeral
-|- OCTAL = BASEN 8
-\ENDTHEOREM
 \THEOREM OCTAL\_11 numeral
 |- !l1 l2.
     IS_OCTAL l1 ==>
@@ -393,6 +387,9 @@
 \THEOREM OCTAL\_DIGIT\_EQ\_DIGIT numeral
 |- !e. OCTAL[e] = e
 \ENDTHEOREM
+\THEOREM OCTAL numeral
+|- OCTAL = BASEN 8
+\ENDTHEOREM
 \THEOREM OCTAL\_EMPTY\_EQ\_0 numeral
 |- !l. IS_NORMALIZED l ==> ((OCTAL l = 0) = (l = []))
 \ENDTHEOREM
--- hol88-2.02.19940316.orig/Library/pred_sets/Manual/entries.tex
+++ hol88-2.02.19940316/Library/pred_sets/Manual/entries.tex
@@ -1,7 +1,4 @@
-\chapter{ML Functions in the Library}
-\label{entries}
-\input{entries-intro}
-\DOC{DELETE\_CONV}
+\chapter{ML Functions in the Library}\label{entries}\input{entries-intro}\DOC{DELETE\_CONV}
 
 \TYPE {\small\verb%DELETE_CONV : conv -> conv%}\egroup
 
@@ -204,6 +201,84 @@
 
 \ENDDOC
 
+\DOC{IN\_CONV}
+
+\TYPE {\small\verb%IN_CONV : conv -> conv%}\egroup
+
+\SYNOPSIS
+Decision procedure for membership in finite sets.
+
+\DESCRIBE 
+The function {\small\verb%IN_CONV%} is a parameterized conversion for proving or disproving
+membership assertions of the general form:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   "t IN {t1,...,tn}"
+\end{verbatim}
+}
+\noindent where {\small\verb%{t1,...,tn}%} is a set of type {\small\verb%ty->bool%} and {\small\verb%t%} is a value
+of the base type {\small\verb%ty%}.  The first argument to {\small\verb%IN_CONV%} is expected to be a
+conversion that decides equality between values of the base type {\small\verb%ty%}.  Given
+an equation {\small\verb%"e1 = e2"%}, where {\small\verb%e1%} and {\small\verb%e2%} are terms of type {\small\verb%ty%}, this
+conversion should return the theorem {\small\verb%|- (e1 = e2) = T%} or the theorem
+{\small\verb%|- (e1 = e2) = F%}, as appropriate.
+
+Given such a conversion, the function {\small\verb%IN_CONV%} returns a conversion that
+maps a term of the form {\small\verb%"t IN {t1,...,tn}"%} to the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- t IN {t1,...,tn} = T
+\end{verbatim}
+}
+
+\noindent if {\small\verb%t%} is alpha-equivalent to any {\small\verb%ti%}, or if the supplied conversion
+proves {\small\verb%|- (t = ti) = T%} for any {\small\verb%ti%}. If the supplied conversion proves
+{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}, then the result is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- t IN {t1,...,tn} = F 
+\end{verbatim}
+}
+\noindent In all other cases, {\small\verb%IN_CONV%} will fail.
+
+\EXAMPLE
+In the following example, the conversion {\small\verb%num_EQ_CONV%} is supplied as a
+parameter and used to test equality of the candidate element {\small\verb%1%} with the
+actual elements of the given set.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV num_EQ_CONV "2 IN {0,SUC 1,3}";;
+   |- 2 IN {0,SUC 1,3} = T
+\end{verbatim}
+}
+\noindent The result is {\small\verb%T%} because {\small\verb%num_EQ_CONV%} is able to prove that {\small\verb%2%} is
+equal to {\small\verb%SUC 1%}. An example of a negative result is:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV num_EQ_CONV "1 IN {0,2,3}";;
+   |- 1 IN {0,2,3} = F
+\end{verbatim}
+}
+\noindent Finally the behaviour of the supplied conversion is irrelevant when
+the value to be tested for membership is alpha-equivalent to an actual element:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #IN_CONV NO_CONV "1 IN {3,2,1}";;
+   |- 1 IN {3,2,1} = T
+\end{verbatim}
+}
+\noindent The conversion {\small\verb%NO_CONV%} always fails, but {\small\verb%IN_CONV%} is nontheless
+able in this case to prove the required result.
+
+\FAILURE
+{\small\verb%IN_CONV conv%} fails if applied to a term that is not of the form {\small\verb%"t IN
+{t1,...,tn}"%}.  A call {\small\verb%IN_CONV conv "t IN {t1,...,tn}"%} fails unless the
+term {\small\verb%t%} is alpha-equivalent to some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
+{\small\verb%|- (t = ti) = T%} for some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
+{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}.
+
+\ENDDOC
+
 \DOC{INSERT\_CONV}
 
 \TYPE {\small\verb%INSERT_CONV : conv -> conv%}\egroup
@@ -290,84 +365,6 @@
 
 \ENDDOC
 
-\DOC{IN\_CONV}
-
-\TYPE {\small\verb%IN_CONV : conv -> conv%}\egroup
-
-\SYNOPSIS
-Decision procedure for membership in finite sets.
-
-\DESCRIBE 
-The function {\small\verb%IN_CONV%} is a parameterized conversion for proving or disproving
-membership assertions of the general form:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   "t IN {t1,...,tn}"
-\end{verbatim}
-}
-\noindent where {\small\verb%{t1,...,tn}%} is a set of type {\small\verb%ty->bool%} and {\small\verb%t%} is a value
-of the base type {\small\verb%ty%}.  The first argument to {\small\verb%IN_CONV%} is expected to be a
-conversion that decides equality between values of the base type {\small\verb%ty%}.  Given
-an equation {\small\verb%"e1 = e2"%}, where {\small\verb%e1%} and {\small\verb%e2%} are terms of type {\small\verb%ty%}, this
-conversion should return the theorem {\small\verb%|- (e1 = e2) = T%} or the theorem
-{\small\verb%|- (e1 = e2) = F%}, as appropriate.
-
-Given such a conversion, the function {\small\verb%IN_CONV%} returns a conversion that
-maps a term of the form {\small\verb%"t IN {t1,...,tn}"%} to the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- t IN {t1,...,tn} = T
-\end{verbatim}
-}
-
-\noindent if {\small\verb%t%} is alpha-equivalent to any {\small\verb%ti%}, or if the supplied conversion
-proves {\small\verb%|- (t = ti) = T%} for any {\small\verb%ti%}. If the supplied conversion proves
-{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}, then the result is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- t IN {t1,...,tn} = F 
-\end{verbatim}
-}
-\noindent In all other cases, {\small\verb%IN_CONV%} will fail.
-
-\EXAMPLE
-In the following example, the conversion {\small\verb%num_EQ_CONV%} is supplied as a
-parameter and used to test equality of the candidate element {\small\verb%1%} with the
-actual elements of the given set.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV num_EQ_CONV "2 IN {0,SUC 1,3}";;
-   |- 2 IN {0,SUC 1,3} = T
-\end{verbatim}
-}
-\noindent The result is {\small\verb%T%} because {\small\verb%num_EQ_CONV%} is able to prove that {\small\verb%2%} is
-equal to {\small\verb%SUC 1%}. An example of a negative result is:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV num_EQ_CONV "1 IN {0,2,3}";;
-   |- 1 IN {0,2,3} = F
-\end{verbatim}
-}
-\noindent Finally the behaviour of the supplied conversion is irrelevant when
-the value to be tested for membership is alpha-equivalent to an actual element:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #IN_CONV NO_CONV "1 IN {3,2,1}";;
-   |- 1 IN {3,2,1} = T
-\end{verbatim}
-}
-\noindent The conversion {\small\verb%NO_CONV%} always fails, but {\small\verb%IN_CONV%} is nontheless
-able in this case to prove the required result.
-
-\FAILURE
-{\small\verb%IN_CONV conv%} fails if applied to a term that is not of the form {\small\verb%"t IN
-{t1,...,tn}"%}.  A call {\small\verb%IN_CONV conv "t IN {t1,...,tn}"%} fails unless the
-term {\small\verb%t%} is alpha-equivalent to some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
-{\small\verb%|- (t = ti) = T%} for some {\small\verb%ti%}, or {\small\verb%conv "t = ti"%} returns
-{\small\verb%|- (t = ti) = F%} for every {\small\verb%ti%}.
-
-\ENDDOC
-
 \DOC{SET\_INDUCT\_TAC}
 
 \TYPE {\small\verb%SET_INDUCT_TAC : tactic%}\egroup
--- hol88-2.02.19940316.orig/Library/res_quan/Manual/entries.tex
+++ hol88-2.02.19940316/Library/res_quan/Manual/entries.tex
@@ -1,6 +1,142 @@
-\chapter{ML Functions in the {\tt res\_quan} Library}
-\label{entries}
-\input{entries-intro}
+\chapter{ML Functions in the {\tt res\_quan} Library}\label{entries}\input{entries-intro}\DOC{COND\_REWR\_CANON}
+
+\TYPE {\small\verb%COND_REWR_CANON : thm -> thm%}\egroup
+
+\SYNOPSIS
+Transform a theorem into a form accepted by {\small\verb%COND_REWR_TAC%}.
+
+\DESCRIBE
+{\small\verb%COND_REWR_CANON%} transforms a theorem into a form accepted by {\small\verb%COND_REWR_TAC%}.
+The input theorem should be an implication of the following form
+{\par\samepage\setseps\small
+\begin{verbatim}
+   !x1 ... xn. P1[xi] ==> ... ==> !y1 ... ym. Pr[xi,yi] ==>
+     (!z1 ... zk. u[xi,yi,zi] = v[xi,yi,zi])
+\end{verbatim}
+}
+\noindent where each antecedent {\small\verb%Pi%} itself may be a conjunction or
+disjunction. The output theorem will have all universal quantifications
+moved to the outer most level with possible renaming to prevent
+variable capture, and have all antecedents which are a conjunction
+transformed to implications. The output theorem will be in the
+following form
+{\par\samepage\setseps\small
+\begin{verbatim}
+   !x1 ... xn y1 ... ym z1 ... zk. 
+    P11[xi] ==> ... ==> P1p[xi] ==> ... ==>
+     Pr1[xi,yi] ==> ... ==> Prq[x1,yi] ==> (u[xi,yi,zi] = v[xi,yi,zi])
+\end{verbatim}
+}
+
+\FAILURE
+This function fails if the input theorem is not in the correct form.
+
+\EXAMPLE
+{\small\verb%COND_REWR_CANON%} transforms the built-in theorem {\small\verb%CANCL_SUB%} into the
+form for conditional rewriting:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #COND_REWR_CANON CANCEL_SUB;;
+   Theorem CANCEL_SUB autoloading from theory `arithmetic` ...
+   CANCEL_SUB = |- !p n m. p <= n /\ p <= m ==> ((n - p = m - p) = (n = m))
+
+   |- !p n m. p <= n ==> p <= m ==> ((n - p = m - p) = (n = m))
+\end{verbatim}
+}
+
+\SEEALSO
+COND_REWRITE1_TAC, COND_REWR_TAC, COND_REWRITE1_CONV, COND_REWR_CONV, 
+search_top_down.
+
+\ENDDOC
+
+\DOC{COND\_REWR\_CONV}
+
+{\small
+\begin{verbatim}
+COND_REWR_CONV : ((term -> term ->
+ ((term # term) list # (type # type) list) list) -> thm -> conv)
+\end{verbatim}
+}\egroup
+
+\SYNOPSIS
+A lower level conversion implementing simple conditional rewriting.
+
+\DESCRIBE
+{\small\verb%COND_REWR_CONV%} is one of the basic building blocks for the
+implementation of the simple conditional rewriting conversions in the
+HOL system. In particular, the conditional term replacement or
+rewriting done by all the conditional 
+rewriting conversions in this library is ultimately done by applications of
+{\small\verb%COND_REWR_CONV%}.  The description given here for {\small\verb%COND_REWR_CONV%} may
+therefore be taken as a specification of the atomic action of
+replacing equals by equals in a term under certain conditions that
+are used in all these higher level conditional rewriting conversions.
+
+The first argument to {\small\verb%COND_REWR_CONV%} is expected to be a function
+which returns a list of matches. Each of these matches is in the form
+of the value returned by the built-in function {\small\verb%match%}. It is used to
+search the input term for instances which may be rewritten.
+
+The second argument to {\small\verb%COND_REWR_CONV%} is expected to be an
+implicative theorem in the following form:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   A |- !x1 ... xn. P1 ==> ... Pm ==> (Q[x1,...,xn] = R[x1,...,xn])
+\end{verbatim}
+}
+\noindent where {\small\verb%x1%}, ..., {\small\verb%xn%} are all the variables that occur free in the
+left hand side of the conclusion of the theorem but do not occur free in the
+assumptions. 
+
+The last argument to {\small\verb%COND_REWR_CONV%} is the term to be rewritten.
+
+If {\small\verb%fn%} is a function and {\small\verb%th%} is an implicative theorem of the kind
+shown above, then {\small\verb%COND_REWR_CONV fn th%} will be a conversion.
+When applying to a term {\small\verb%tm%}, it will return a theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   P1', ..., Pm' |- tm = tm[R'/Q']
+\end{verbatim}
+}
+\noindent if evaluating {\small\verb%fn Q[x1,...,xn] tm%} returns a
+non-empty list of matches.
+The assumptions of the resulting theorem are instances of the
+antecedents of the input theorem {\small\verb%th%}. The right hand side of the
+equation is obtained by rewriting the input term {\small\verb%tm%} with instances of
+the conclusion of the input theorem.
+
+\FAILURE
+{\small\verb%COND_REWR_CONV fn th%} fails if {\small\verb%th%} is not an implication of the form
+described above.  If {\small\verb%th%} is such an equation, but the function {\small\verb%fn%}
+returns a null list of matches, or the function {\small\verb%fn%} returns a
+non-empty list of matches, but the term or type instantiation fails.
+
+\EXAMPLE
+The following example illustrates a straightforward use of {\small\verb%COND_REWR_CONV%}.
+We use the built-in theorem {\small\verb%LESS_MOD%} as the input theorem, and the function
+{\small\verb%search_top_down%} as the search function.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #LESS_MOD;;
+   Theorem LESS_MOD autoloading from theory `arithmetic` ...
+   LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
+
+   |- !n k. k < n ==> (k MOD n = k)
+
+   #search_top_down;;
+   - : (term -> term -> ((term # term) list # (type # type) list) list)
+
+   #COND_REWR_CONV search_top_down LESS_MOD "2 MOD 3";;
+   2 < 3 |- 2 MOD 3 = 2
+\end{verbatim}
+}
+
+\SEEALSO
+COND_REWR_TAC, COND_REWRITE1_TAC, COND_REWRITE1_CONV, COND_REWR_CANON,
+search_top_down.
+
+\ENDDOC
 \DOC{COND\_REWRITE1\_CONV}
 
 \TYPE {\small\verb%COND_REWRITE1_CONV : (thm list -> thm -> conv)%}\egroup
@@ -147,145 +283,6 @@
 
 \ENDDOC
 
-\DOC{COND\_REWR\_CANON}
-
-\TYPE {\small\verb%COND_REWR_CANON : thm -> thm%}\egroup
-
-\SYNOPSIS
-Transform a theorem into a form accepted by {\small\verb%COND_REWR_TAC%}.
-
-\DESCRIBE
-{\small\verb%COND_REWR_CANON%} transforms a theorem into a form accepted by {\small\verb%COND_REWR_TAC%}.
-The input theorem should be an implication of the following form
-{\par\samepage\setseps\small
-\begin{verbatim}
-   !x1 ... xn. P1[xi] ==> ... ==> !y1 ... ym. Pr[xi,yi] ==>
-     (!z1 ... zk. u[xi,yi,zi] = v[xi,yi,zi])
-\end{verbatim}
-}
-\noindent where each antecedent {\small\verb%Pi%} itself may be a conjunction or
-disjunction. The output theorem will have all universal quantifications
-moved to the outer most level with possible renaming to prevent
-variable capture, and have all antecedents which are a conjunction
-transformed to implications. The output theorem will be in the
-following form
-{\par\samepage\setseps\small
-\begin{verbatim}
-   !x1 ... xn y1 ... ym z1 ... zk. 
-    P11[xi] ==> ... ==> P1p[xi] ==> ... ==>
-     Pr1[xi,yi] ==> ... ==> Prq[x1,yi] ==> (u[xi,yi,zi] = v[xi,yi,zi])
-\end{verbatim}
-}
-
-\FAILURE
-This function fails if the input theorem is not in the correct form.
-
-\EXAMPLE
-{\small\verb%COND_REWR_CANON%} transforms the built-in theorem {\small\verb%CANCL_SUB%} into the
-form for conditional rewriting:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #COND_REWR_CANON CANCEL_SUB;;
-   Theorem CANCEL_SUB autoloading from theory `arithmetic` ...
-   CANCEL_SUB = |- !p n m. p <= n /\ p <= m ==> ((n - p = m - p) = (n = m))
-
-   |- !p n m. p <= n ==> p <= m ==> ((n - p = m - p) = (n = m))
-\end{verbatim}
-}
-
-\SEEALSO
-COND_REWRITE1_TAC, COND_REWR_TAC, COND_REWRITE1_CONV, COND_REWR_CONV, 
-search_top_down.
-
-\ENDDOC
-
-\DOC{COND\_REWR\_CONV}
-
-{\small
-\begin{verbatim}
-COND_REWR_CONV : ((term -> term ->
- ((term # term) list # (type # type) list) list) -> thm -> conv)
-\end{verbatim}
-}\egroup
-
-\SYNOPSIS
-A lower level conversion implementing simple conditional rewriting.
-
-\DESCRIBE
-{\small\verb%COND_REWR_CONV%} is one of the basic building blocks for the
-implementation of the simple conditional rewriting conversions in the
-HOL system. In particular, the conditional term replacement or
-rewriting done by all the conditional 
-rewriting conversions in this library is ultimately done by applications of
-{\small\verb%COND_REWR_CONV%}.  The description given here for {\small\verb%COND_REWR_CONV%} may
-therefore be taken as a specification of the atomic action of
-replacing equals by equals in a term under certain conditions that
-are used in all these higher level conditional rewriting conversions.
-
-The first argument to {\small\verb%COND_REWR_CONV%} is expected to be a function
-which returns a list of matches. Each of these matches is in the form
-of the value returned by the built-in function {\small\verb%match%}. It is used to
-search the input term for instances which may be rewritten.
-
-The second argument to {\small\verb%COND_REWR_CONV%} is expected to be an
-implicative theorem in the following form:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   A |- !x1 ... xn. P1 ==> ... Pm ==> (Q[x1,...,xn] = R[x1,...,xn])
-\end{verbatim}
-}
-\noindent where {\small\verb%x1%}, ..., {\small\verb%xn%} are all the variables that occur free in the
-left hand side of the conclusion of the theorem but do not occur free in the
-assumptions. 
-
-The last argument to {\small\verb%COND_REWR_CONV%} is the term to be rewritten.
-
-If {\small\verb%fn%} is a function and {\small\verb%th%} is an implicative theorem of the kind
-shown above, then {\small\verb%COND_REWR_CONV fn th%} will be a conversion.
-When applying to a term {\small\verb%tm%}, it will return a theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   P1', ..., Pm' |- tm = tm[R'/Q']
-\end{verbatim}
-}
-\noindent if evaluating {\small\verb%fn Q[x1,...,xn] tm%} returns a
-non-empty list of matches.
-The assumptions of the resulting theorem are instances of the
-antecedents of the input theorem {\small\verb%th%}. The right hand side of the
-equation is obtained by rewriting the input term {\small\verb%tm%} with instances of
-the conclusion of the input theorem.
-
-\FAILURE
-{\small\verb%COND_REWR_CONV fn th%} fails if {\small\verb%th%} is not an implication of the form
-described above.  If {\small\verb%th%} is such an equation, but the function {\small\verb%fn%}
-returns a null list of matches, or the function {\small\verb%fn%} returns a
-non-empty list of matches, but the term or type instantiation fails.
-
-\EXAMPLE
-The following example illustrates a straightforward use of {\small\verb%COND_REWR_CONV%}.
-We use the built-in theorem {\small\verb%LESS_MOD%} as the input theorem, and the function
-{\small\verb%search_top_down%} as the search function.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #LESS_MOD;;
-   Theorem LESS_MOD autoloading from theory `arithmetic` ...
-   LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
-
-   |- !n k. k < n ==> (k MOD n = k)
-
-   #search_top_down;;
-   - : (term -> term -> ((term # term) list # (type # type) list) list)
-
-   #COND_REWR_CONV search_top_down LESS_MOD "2 MOD 3";;
-   2 < 3 |- 2 MOD 3 = 2
-\end{verbatim}
-}
-
-\SEEALSO
-COND_REWR_TAC, COND_REWRITE1_TAC, COND_REWRITE1_CONV, COND_REWR_CANON,
-search_top_down.
-
-\ENDDOC
 \DOC{COND\_REWR\_TAC}
 
 {\small
@@ -553,6 +550,36 @@
 mk_resq_select, is_resq_select, strip_resq_select.
 
 \ENDDOC
+\DOC{GQSPEC\_ALL}
+
+\TYPE {\small\verb%GQSPEC_ALL : (thm -> thm)%}\egroup
+
+\SYNOPSIS
+Specializes the conclusion of a theorem with its own quantified variables.
+
+\DESCRIBE
+When applied to a theorem whose conclusion has zero or more 
+ordinary or restricted universal quantifications,
+the inference rule {\small\verb%GQSPEC_ALL%} returns a theorem which is the result
+of specializing the quantified variables with its own variables. If this
+will cause name clashes, a variant of the variable is used instead.
+Normally {\small\verb%xi'%} is just {\small\verb%xi%}, in which case {\small\verb%GQSPEC_ALL%} simply removes
+all universal quantifiers.
+{\par\samepage\setseps\small
+\begin{verbatim}
+       A |- !x1::P1. ...!xk. ... !xn::Pn. t
+   ------------------------------------------------------  GQSPEC_ALL
+    A,P1 x1,...,Pn xn |- t[x1'/x1]...[xk'/xk]...[xn'/xn]
+\end{verbatim}
+}
+\FAILURE
+Never fails.
+
+\SEEALSO
+GQSPEC, GQSPECL, SPEC, SPECL, SPEC_ALL, RESQ_GEN, RESQ_GENL,
+RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPECL, RESQ_SPEC_ALL.
+
+\ENDDOC
 \DOC{GQSPECL}
 
 \TYPE {\small\verb%GQSPECL : (term list -> thm -> thm)%}\egroup
@@ -588,36 +615,6 @@
 RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPECL, RESQ_SPEC_ALL.
 
 \ENDDOC
-\DOC{GQSPEC\_ALL}
-
-\TYPE {\small\verb%GQSPEC_ALL : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Specializes the conclusion of a theorem with its own quantified variables.
-
-\DESCRIBE
-When applied to a theorem whose conclusion has zero or more 
-ordinary or restricted universal quantifications,
-the inference rule {\small\verb%GQSPEC_ALL%} returns a theorem which is the result
-of specializing the quantified variables with its own variables. If this
-will cause name clashes, a variant of the variable is used instead.
-Normally {\small\verb%xi'%} is just {\small\verb%xi%}, in which case {\small\verb%GQSPEC_ALL%} simply removes
-all universal quantifiers.
-{\par\samepage\setseps\small
-\begin{verbatim}
-       A |- !x1::P1. ...!xk. ... !xn::Pn. t
-   ------------------------------------------------------  GQSPEC_ALL
-    A,P1 x1,...,Pn xn |- t[x1'/x1]...[xk'/xk]...[xn'/xn]
-\end{verbatim}
-}
-\FAILURE
-Never fails.
-
-\SEEALSO
-GQSPEC, GQSPECL, SPEC, SPECL, SPEC_ALL, RESQ_GEN, RESQ_GENL,
-RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPECL, RESQ_SPEC_ALL.
-
-\ENDDOC
 \DOC{IMP\_RESQ\_FORALL\_CONV}
 
 \TYPE {\small\verb%IMP_RESQ_FORALL_CONV : conv%}\egroup
@@ -1216,6 +1213,31 @@
 RESQ_FORALL_CONV.
 
 \ENDDOC
+\DOC{RESQ\_GEN\_ALL}
+
+\TYPE {\small\verb%RESQ_GEN_ALL : (thm -> thm)%}\egroup
+
+\SYNOPSIS
+Generalizes the conclusion of a theorem over its own assumptions.
+
+\DESCRIBE
+When applied to a theorem {\small\verb%A |- t%}, the inference rule {\small\verb%RESQ_GEN_ALL%} returns
+the theorem {\small\verb%A' |- !x1::P1. ...!xn::Pn. t%}, where the {\small\verb%Pi xi%} are in the 
+assumptions.
+{\par\samepage\setseps\small
+\begin{verbatim}
+         A |- t
+   ------------------------------------------------  RESQ_GEN_ALL
+   A - (P1 x1,...,Pn xn) |- !x1::P1. ... !xn::Pn. t
+\end{verbatim}
+}
+\FAILURE
+Never fails.
+
+\SEEALSO
+RESQ_GEN, RESQ_GENL, GEN_ALL, RESQ_SPEC, RESQ_SPECL, RESQ_SPEC_ALL.
+
+\ENDDOC
 \DOC{RESQ\_GEN}
 
 \TYPE {\small\verb%RESQ_GEN : ((term # term) -> thm -> thm)%}\egroup
@@ -1274,31 +1296,6 @@
 RESQ_GEN, RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPECL, RESQ_SPEC_ALL.
 
 \ENDDOC
-\DOC{RESQ\_GEN\_ALL}
-
-\TYPE {\small\verb%RESQ_GEN_ALL : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Generalizes the conclusion of a theorem over its own assumptions.
-
-\DESCRIBE
-When applied to a theorem {\small\verb%A |- t%}, the inference rule {\small\verb%RESQ_GEN_ALL%} returns
-the theorem {\small\verb%A' |- !x1::P1. ...!xn::Pn. t%}, where the {\small\verb%Pi xi%} are in the 
-assumptions.
-{\par\samepage\setseps\small
-\begin{verbatim}
-         A |- t
-   ------------------------------------------------  RESQ_GEN_ALL
-   A - (P1 x1,...,Pn xn) |- !x1::P1. ... !xn::Pn. t
-\end{verbatim}
-}
-\FAILURE
-Never fails.
-
-\SEEALSO
-RESQ_GEN, RESQ_GENL, GEN_ALL, RESQ_SPEC, RESQ_SPECL, RESQ_SPEC_ALL.
-
-\ENDDOC
 \DOC{RESQ\_GEN\_TAC}
 
 \TYPE {\small\verb%RESQ_GEN_TAC : tactic%}\egroup
@@ -1571,6 +1568,40 @@
 IMP_RES_THEN, IMP_RES_TAC, MATCH_MP, RES_CANON, RES_TAC, RES_THEN.
 
 \ENDDOC
+\DOC{RESQ\_REWR\_CANON}
+
+\TYPE {\small\verb%RESQ_REWR_CANON : thm -> thm%}\egroup
+
+\SYNOPSIS
+Transform a theorem into a form accepted for rewriting.
+
+\DESCRIBE
+{\small\verb%RESQ_REWR_CANON%} transforms a theorem into a form accepted by {\small\verb%COND_REWR_TAC%}.
+The input theorem should be headed by a series of restricted universal
+quantifications in the following form
+{\par\samepage\setseps\small
+\begin{verbatim}
+   !x1::P1. ... !xn::Pn. u[xi] = v[xi])
+\end{verbatim}
+}
+\noindent Other variables occurring in {\small\verb%u%} and {\small\verb%v%} may be universally quantified.
+The output theorem will have all ordinary universal quantifications
+moved to the outer most level with possible renaming to prevent
+variable capture, and have all restricted universal quantifications
+converted to implications. The output theorem will be in the
+form accepted by {\small\verb%COND_REWR_TAC%}.
+
+\FAILURE
+This function fails is the input theorem is not in the correct form.
+
+
+\SEEALSO
+RESQ_REWRITE1_TAC, RESQ_REWRITE1_CONV,
+COND_REWR_CANON, COND_REWR_TAC, COND_REWR_CONV,.
+
+
+\ENDDOC
+
 \DOC{RESQ\_REWRITE1\_CONV}
 
 \TYPE {\small\verb%RESQ_REWRITE1_CONV : thm list -> thm -> conv%}\egroup
@@ -1656,40 +1687,38 @@
 
 \ENDDOC
 
-\DOC{RESQ\_REWR\_CANON}
+\DOC{RESQ\_SPEC\_ALL}
 
-\TYPE {\small\verb%RESQ_REWR_CANON : thm -> thm%}\egroup
+\TYPE {\small\verb%RESQ_SPEC_ALL : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Transform a theorem into a form accepted for rewriting.
+Specializes the conclusion of a theorem with its own restricted
+quantified variables.
 
 \DESCRIBE
-{\small\verb%RESQ_REWR_CANON%} transforms a theorem into a form accepted by {\small\verb%COND_REWR_TAC%}.
-The input theorem should be headed by a series of restricted universal
-quantifications in the following form
+When applied to a theorem {\small\verb%A |- !x1::P1. ...!xn::Pn. t%},
+the inference rule {\small\verb%RESQ_SPEC_ALL%}
+returns the theorem {\small\verb%A,P1 x1',...,Pn xn' |- t[x1'/x1]...[xn'/xn]%}
+ where the {\small\verb%xi'%} are distinct
+variants of the corresponding {\small\verb%xi%}, chosen to avoid clashes with any variables
+free in the assumption list and with the names of constants. Normally {\small\verb%xi'%} is
+just {\small\verb%xi%}, in which case {\small\verb%RESQ_SPEC_ALL%} simply removes all restricted
+ universal quantifiers.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   !x1::P1. ... !xn::Pn. u[xi] = v[xi])
+       A |- !x1::P1. ... !xn::Pn. t
+   -------------------------------------------  RESQ_SPEC_ALL
+    A,P1 x1,...,Pn xn |- t[x1'/x1]...[xn'/xn]
 \end{verbatim}
 }
-\noindent Other variables occurring in {\small\verb%u%} and {\small\verb%v%} may be universally quantified.
-The output theorem will have all ordinary universal quantifications
-moved to the outer most level with possible renaming to prevent
-variable capture, and have all restricted universal quantifications
-converted to implications. The output theorem will be in the
-form accepted by {\small\verb%COND_REWR_TAC%}.
 
 \FAILURE
-This function fails is the input theorem is not in the correct form.
-
+Never fails.
 
 \SEEALSO
-RESQ_REWRITE1_TAC, RESQ_REWRITE1_CONV,
-COND_REWR_CANON, COND_REWR_TAC, COND_REWR_CONV,.
-
+RESQ_GEN, RESQ_GENL, RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPECL.
 
 \ENDDOC
-
 \DOC{RESQ\_SPEC}
 
 \TYPE {\small\verb%RESQ_SPEC : (term -> thm -> thm)%}\egroup
@@ -1769,38 +1798,6 @@
 RESQ_GEN, RESQ_GENL, RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPEC_ALL.
 
 \ENDDOC
-\DOC{RESQ\_SPEC\_ALL}
-
-\TYPE {\small\verb%RESQ_SPEC_ALL : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Specializes the conclusion of a theorem with its own restricted
-quantified variables.
-
-\DESCRIBE
-When applied to a theorem {\small\verb%A |- !x1::P1. ...!xn::Pn. t%},
-the inference rule {\small\verb%RESQ_SPEC_ALL%}
-returns the theorem {\small\verb%A,P1 x1',...,Pn xn' |- t[x1'/x1]...[xn'/xn]%}
- where the {\small\verb%xi'%} are distinct
-variants of the corresponding {\small\verb%xi%}, chosen to avoid clashes with any variables
-free in the assumption list and with the names of constants. Normally {\small\verb%xi'%} is
-just {\small\verb%xi%}, in which case {\small\verb%RESQ_SPEC_ALL%} simply removes all restricted
- universal quantifiers.
-{\par\samepage\setseps\small
-\begin{verbatim}
-       A |- !x1::P1. ... !xn::Pn. t
-   -------------------------------------------  RESQ_SPEC_ALL
-    A,P1 x1,...,Pn xn |- t[x1'/x1]...[xn'/xn]
-\end{verbatim}
-}
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-RESQ_GEN, RESQ_GENL, RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC, RESQ_SPECL.
-
-\ENDDOC
 \DOC{search\_top\_down}
 
 {\small
--- hol88-2.02.19940316.orig/Library/res_quan/Manual/theorems.tex
+++ hol88-2.02.19940316/Library/res_quan/Manual/theorems.tex
@@ -1,6 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\THEOREM DISJ\_RESQ\_EXISTS\_DIST res\_quan
+\chapter{Pre-proved Theorems}\input{theorems-intro}\THEOREM DISJ\_RESQ\_EXISTS\_DIST res\_quan
 |- !P Q R.
    (?i :: \i. P i \/ Q i. R i) = (?i :: P. R i) \/ (?i :: Q. R i)
 \ENDTHEOREM
--- hol88-2.02.19940316.orig/debian/compat
+++ hol88-2.02.19940316/debian/compat
@@ -0,0 +1 @@
+5
--- hol88-2.02.19940316.orig/debian/gcl_patch.l
+++ hol88-2.02.19940316/debian/gcl_patch.l
@@ -0,0 +1,72 @@
+(in-package 'compiler)
+(defun make-user-init (files outn)
+
+  (let* ((c (pathname outn))
+	 (c (merge-pathnames c (make-pathname :directory '(:current))))
+	 (o (merge-pathnames (make-pathname :type "o") c))
+	 (c (merge-pathnames (make-pathname :type "c") c)))
+  
+  (with-open-file (st c :direction :output)
+		  (format st "#include ~a~%~%" *cmpinclude*)
+
+		  (format st "#define load2(a) do {")
+		  (format st "printf(\"Loading %s...\\n\",(a));")
+		  (format st "load(a);")
+		  (format st "printf(\"Finished %s...\\n\",(a));} while(0)~%~%")
+
+		  (let ((p nil))
+		    (dolist (tem files)
+		      (when (equal (pathname-type tem) "o")
+			(let ((tem (namestring tem)))
+			  (push (list (si::find-init-name tem) tem) p))))
+
+		    (setq p (nreverse p))
+
+		    (dolist (tem p)
+		      (format st "extern void ~a(void);~%" (car tem)))
+		    (format st "~%")
+
+		    (format st "typedef struct {void (*fn)(void);char *s;} Fnlst;~%")
+		    (format st "#define NF ~a~%" (length p))
+		    (format st "static Fnlst my_fnlst[NF]={")
+		    (dolist (tem p)
+		      (when (not (eq tem (car p)))
+			(format st ",~%"))
+		      (format st "{~a,\"~a\"}" (car tem) (cadr tem)))
+		    (format st "};~%~%")
+		    
+		    (format st "static int user_init_run;~%")
+		    (format st "#define my_load(a_,b_) {if (!user_init_run && (a_)) gcl_init_or_load1((a_),(b_));(a_)=0;}~%~%")
+                    
+		    (format st "object user_init(void) {~%")
+		    (format st "user_init_run=1;~%")
+		    (dolist (tem files)
+		      (let ((tem (namestring tem)))
+			    (cond ((equal (cadr (car p)) tem)
+				   (format st "gcl_init_or_load1(~a,\"~a\");~%"
+					   (car (car p)) tem)
+				   (setq p (cdr p)))
+				  (t 
+				   (format st "load2(\"~a\");~%" tem)))))
+		    (format st "return Cnil;}~%~%")
+
+		    (format st "int user_match(const char *s,int n) {~%")
+		    (format st "  Fnlst *f;~%")
+		    (format st "  for (f=my_fnlst;f<my_fnlst+NF;f++){~%")
+		    (format st "     if (!strncmp(s,f->s,n)) {~%")
+		    (format st "        my_load(f->fn,f->s);~%")
+		    (format st "        return 1;~%")
+		    (format st "     }~%")
+		    (format st "  }~%")
+		    (format st "  return 0;~%")
+		    (format st "}~%~%")))
+		    
+  (compiler-cc c o)
+;  (system (format nil "~a ~a" *cc* tem))
+;   (with-open-file (s c) (si::copy-stream s *standard-output*))
+  (delete-file c)
+
+  o))
+(setq *default-system-p* t)
+(in-package 'user)
+(delete :native-reloc *features*)
--- hol88-2.02.19940316.orig/debian/control
+++ hol88-2.02.19940316/debian/control
@@ -0,0 +1,104 @@
+Source: hol88
+Section: math
+Priority: optional
+Maintainer: Camm Maguire <camm@debian.org>
+Build-Depends: debhelper (>= 5), gcl (>= 2.6.7-62), texlive-latex-base, libgmp3-dev, libncurses5-dev, libreadline-dev, libxmu-dev, libxaw7-dev
+Standards-Version: 3.9.1
+
+Package: hol88
+Architecture: any
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, system image
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-source
+Architecture: all
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, source files
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-help
+Architecture: all
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, online help files
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-library
+Architecture: any
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, binary library modules
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-library-source
+Architecture: all
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, library source files
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-library-help
+Architecture: all
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, library online help files
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-contrib-source
+Architecture: all
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, user contributed source
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-contrib-help
+Architecture: all
+Depends: ${shlibs:Depends}, ${misc:Depends}
+Description: Higher Order Logic, user contributed online help files
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
+
+Package: hol88-doc
+Architecture: all
+Description: Documentation for hol88
+ The HOL System is an environment for interactive theorem proving in a
+ higher-order logic. Its most outstanding feature is its high degree
+ of programmability through the meta-language ML. The system has a
+ wide variety of uses from formalizing pure mathematics to
+ verification of industrial hardware. Academic and industrial sites
+ world-wide are using HOL.
--- hol88-2.02.19940316.orig/debian/hol88.manpages
+++ hol88-2.02.19940316/debian/hol88.manpages
@@ -0,0 +1 @@
+debian/hol88.1
--- hol88-2.02.19940316.orig/debian/hol88.1
+++ hol88-2.02.19940316/debian/hol88.1
@@ -0,0 +1,35 @@
+.\"                                      Hey, EMACS: -*- nroff -*-
+.\" First parameter, NAME, should be all caps
+.\" Second parameter, SECTION, should be 1-8, maybe w/ subsection
+.\" other parameters are allowed: see man(7), man(1)
+.TH HOL88 1 "October 26, 2006"
+.\" Please adjust this date whenever revising the manpage.
+.\"
+.\" Some roff macros, for reference:
+.\" .nh        disable hyphenation
+.\" .hy        enable hyphenation
+.\" .ad l      left justify
+.\" .ad b      justify to both left and right margins
+.\" .nf        disable filling
+.\" .fi        enable filling
+.\" .br        insert line break
+.\" .sp <n>    insert n+1 empty lines
+.\" for manpage-specific macros, see man(7)
+.SH NAME
+hol88 \- Higher Order Logic
+.SH SYNOPSIS
+.B hol88
+.SH DESCRIPTION
+This manual page documents briefly the
+.B hol88
+command.
+This manual page was written for the Debian GNU/Linux distribution
+because the original program does not have a manual page.  Instead, it
+has online documentation provided via the hol88-help and
+hol88-library-help packages, and in dvi format as provided in the
+hol88-doc package.  The documentation can also be found at the
+project's website, http://www.ftp.cl.cam.ac.uk/ftp/hvg/hol88, in
+various forms.
+.SH AUTHOR
+This manual page was written by Camm Maguire, <camm@enhanced.com>,
+for the Debian GNU/Linux system (but may be used by others).
--- hol88-2.02.19940316.orig/debian/rules
+++ hol88-2.02.19940316/debian/rules
@@ -0,0 +1,214 @@
+#!/usr/bin/make -f
+# -*- makefile -*-
+# Sample debian/rules that uses debhelper.
+#
+# This file was originally written by Joey Hess and Craig Small.
+# As a special exception, when this file is copied by dh-make into a
+# dh-make output file, you may use that output file without restriction.
+# This special exception was added by Craig Small in version 0.37 of dh-make.
+#
+# Modified to make a template file for a multi-binary package with separated
+# build-arch and build-indep targets  by Bill Allombert 2001
+
+# Uncomment this to turn on verbose mode.
+#export DH_VERBOSE=1
+
+# This has to be exported to make some magic below work.
+export DH_OPTIONS
+
+PN:=hol88
+VR:=$(shell awk '{if (i) next;i=1;a=$$2;gsub("[()]","",a);split(a,A,"-");print A[1];}' debian/changelog)
+PD:=$(PN)-$(VR)
+
+CFLAGS = -Wall -g
+
+ifneq (,$(findstring noopt,$(DEB_BUILD_OPTIONS)))
+	CFLAGS += -O0
+else
+	CFLAGS += -O2
+endif
+
+configure: configure-stamp
+configure-stamp:
+	dh_testdir
+	cat debian/dash.p | patch -p1
+	touch configure-stamp
+
+
+build: build-arch build-indep
+
+build-arch: build-arch-stamp
+build-arch-stamp: configure-stamp 
+
+	echo '#-native-reloc(bye -1)' | gcl || cat debian/gcl_patch.l debian/gcl_save.l | gcl
+	PATH=$$(pwd):$$PATH $(MAKE) all
+	find -name "raw_*_map" -exec rm {} \;
+	for i in $$(find -maxdepth 1 -name "*hol*"); do \
+		printf 'install `'/usr/share/$(PD)'`;;\nlisp `(ml-save "foo")`;;\n' | ./$$i &&\
+		mv foo $$i; done
+	touch $@
+
+build-indep: build-indep-stamp
+build-indep-stamp: configure-stamp 
+
+
+	for i in Manual/Tutorial/ack.tex Manual/Reference/ack.tex Manual/Description/ack.tex; do\
+		ln -snf ../Latex/ack.tex $$i ; done
+	for i in $$(find Library -name index.tex) Library/pred_sets/Manual/theorems.tex Library/record_proof/Manual/record_proof.ind ; do\
+		[ -e $$i.sve ] || cp $$i $$i.sve ; done
+	$(MAKE) -C Manual all
+	touch $@
+
+INSTALLA:=$(addprefix debian/,$(addsuffix .install,\
+	hol88 hol88-library))
+INSTALLI:=$(addprefix debian/,$(addsuffix .install,\
+	hol88-source hol88-help hol88-library-source\
+	hol88-library-help hol88-contrib-source hol88-contrib-help hol88-doc))
+LINKS:=$(addprefix debian/,$(addsuffix .links,hol88 hol88-library))
+
+clean:
+	dh_testdir
+	dh_testroot
+
+	! [ -e configure-stamp ] || cat debian/dash.p | patch -p1 -R
+	rm -f build-arch-stamp build-indep-stamp configure-stamp
+
+	[ ! -f Makefile ] || $(MAKE) clean
+	[ ! -f Makefile ] || $(MAKE) clobber
+	for i in $$(find Library -name index.tex) Library/pred_sets/Manual/theorems.tex Library/record_proof/Manual/record_proof.ind ; do\
+		[ -e $$i.sve ] || cp $$i $$i.sve ; done
+	[ ! -f Makefile ] || $(MAKE) -C Manual clean
+
+	[ ! -f Makefile ] || for i in $$(find Library -name Manual); do $(MAKE) -C $$i clean ; done
+	find -name X.tex -exec rm -rf {} \;
+
+	dh_clean -X./ml/site.ml.orig -X./contrib/tooltool/Makefile.orig \
+		 -X./contrib/tooltool/events.c.orig -X./contrib/tooltool/func_fix.c.orig \
+	         -X./contrib/tooltool/lex.c.orig -X./contrib/tooltool/parse.y.orig \
+		 -X./contrib/tooltool/patchlevel.h.orig -X./contrib/tooltool/windows.c.orig \
+		 -X./contrib/Xhelp/hol_apro.orig -X./contrib/Xhelp/hol_ref.orig \
+		 -X./contrib/Xhelp/xholhelp.h.orig -X./contrib/Xhelp/hol_thm.orig
+
+	for i in $$(find Library -name "*.sve") ; do mv $$i $$(echo $$i | sed "s,\.sve,,1"); done
+
+	rm -f $(INSTALLA) $(INSTALLI) $(LINKS) debian/hol88.sh
+	find -name "*.dvi" -exec rm {} \;
+	rm -f Manual/Tutorial/ack.tex Manual/Reference/ack.tex Manual/Description/ack.tex
+	rm -f Manual/Covers/titlepages.ps Manual/Covers/endpages.ps
+	rm -f bm.l foo* gcl
+	cp debian/site_ml_orig ml/site.ml.orig
+
+
+debian/hol88.install:: 
+	find -maxdepth 1 -name "*hol*" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/lib/$(PD)/%s\n",$$1,a);}' >>$@
+	echo debian/hol88.sh usr/bin >>$@
+debian/hol88-source.install:: 
+	find lisp -name "*.l" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+	find ml -type f -name "*ml" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+	find theories -type f -name "*ml" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+	find theories -type f -name "*th" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+debian/hol88-help.install:: 
+	find help -name "*.doc" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+
+debian/hol88-library.install:: 
+	find Library -name "*.o" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/lib/$(PD)/%s\n",$$1,a);}' >>$@
+debian/hol88-library-source.install:: 
+	find Library -name "*.ml" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+debian/hol88-library-help.install:: 
+	find Library -name "*.doc" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+
+debian/hol88-contrib-source.install:: 
+	find contrib -name "*.ml" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+	find contrib -name "Makefile" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+debian/hol88-contrib-help.install:: 
+	find contrib -name "*.doc" | awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/$(PD)/%s\n",$$1,a);}' >>$@
+
+debian/hol88-doc.install:: 
+	find Manual -name "*dvi" | grep -v makeindex | grep -v psfig | \
+		awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/doc/hol88-doc/%s\n",$$1,a);}' >>$@
+	find Manual -name "*ps" | grep -v makeindex | grep -v psfig | \
+		awk '{a=$$1;sub("/[^/]*$$","",a);printf("%s usr/share/doc/hol88-doc/%s\n",$$1,a);}' >>$@
+
+
+debian/hol88.links:: 
+	find * -maxdepth 0 -name "*hol*" | awk '{printf("/usr/lib/$(PD)/%s usr/share/$(PD)/%s\n",$$1,$$1);}' >>$@
+debian/hol88-library.links:: 
+	find Library -name "*.o" | awk '{printf("/usr/lib/$(PD)/%s usr/share/$(PD)/%s\n",$$1,$$1);}' >>$@
+
+
+debian/hol88.sh:
+	echo "#!/bin/bash" >$@
+	echo >>$@
+	echo "exec /usr/lib/$(PD)/hol" >>$@
+	chmod 755 $@
+
+
+install: install-indep install-arch
+install-indep: $(INSTALLI)
+	dh_testdir
+	dh_testroot
+	dh_clean -k -i -X./ml/site.ml.orig -X./contrib/tooltool/Makefile.orig \
+		 -X./contrib/tooltool/events.c.orig -X./contrib/tooltool/func_fix.c.orig \
+	         -X./contrib/tooltool/lex.c.orig -X./contrib/tooltool/parse.y.orig \
+		 -X./contrib/tooltool/patchlevel.h.orig -X./contrib/tooltool/windows.c.orig \
+		 -X./contrib/Xhelp/hol_apro.orig -X./contrib/Xhelp/hol_ref.orig \
+		 -X./contrib/Xhelp/xholhelp.h.orig -X./contrib/Xhelp/hol_thm.orig
+
+	dh_installdirs -i
+
+	dh_install -i
+
+install-arch: $(INSTALLA) $(LINKS) debian/hol88.sh
+	dh_testdir
+	dh_testroot
+	dh_clean -k -s -X./ml/site.ml.orig -X./contrib/tooltool/Makefile.orig \
+		 -X./contrib/tooltool/events.c.orig -X./contrib/tooltool/func_fix.c.orig \
+	         -X./contrib/tooltool/lex.c.orig -X./contrib/tooltool/parse.y.orig \
+		 -X./contrib/tooltool/patchlevel.h.orig -X./contrib/tooltool/windows.c.orig \
+		 -X./contrib/Xhelp/hol_apro.orig -X./contrib/Xhelp/hol_ref.orig \
+		 -X./contrib/Xhelp/xholhelp.h.orig -X./contrib/Xhelp/hol_thm.orig
+
+	dh_installdirs -s
+
+	dh_install -s
+
+	mv debian/hol88/usr/bin/hol88.sh debian/hol88/usr/bin/hol88
+
+binary-common:
+	dh_testdir
+	dh_testroot
+	dh_installchangelogs 
+	dh_installdocs
+	dh_installexamples
+#	dh_installmenu
+#	dh_installdebconf	
+#	dh_installlogrotate	
+#	dh_installemacsen
+#	dh_installpam
+#	dh_installmime
+#	dh_python
+#	dh_installinit
+#	dh_installcron
+#	dh_installinfo
+	dh_installman
+	dh_link
+	dh_strip
+	dh_compress 
+	dh_fixperms
+#	dh_perl
+	dh_makeshlibs
+	dh_installdeb
+	dh_shlibdeps
+	dh_gencontrol
+	dh_md5sums
+	dh_builddeb
+# Build architecture independant packages using the common target.
+binary-indep: build-indep install-indep
+	$(MAKE) -f debian/rules DH_OPTIONS=-i binary-common
+
+# Build architecture dependant packages using the common target.
+binary-arch: build-arch install-arch
+	$(MAKE) -f debian/rules DH_OPTIONS=-s binary-common
+
+binary: binary-arch binary-indep
+.PHONY: build clean binary-indep binary-arch binary install install-indep install-arch configure
--- hol88-2.02.19940316.orig/debian/dash.p
+++ hol88-2.02.19940316/debian/dash.p
@@ -0,0 +1,931 @@
+--- a/Library/abs_theory/Manual/Makefile
++++ b/Library/abs_theory/Manual/Makefile
+@@ -15,13 +15,13 @@
+ 
+ clean:;                                                                 \
+     rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex;              \
+-    echo "\begin{theindex}" >index.tex;                                 \
+-    echo "\mbox{}" >>index.tex;                                         \
+-    echo "\end{theindex}" >>index.tex
++    printf '\\begin{theindex}' >index.tex;                                 \
++    printf '\\mbox{}' >>index.tex;                                         \
++    printf '\\end{theindex}' >>index.tex
+ 
+ ids:;                                                                   \
+-    echo "\chapter{ML Functions in the {\tt abs\_theory} Library}" >entries.tex;   \
+-    echo "\input{entries-intro}" >>entries.tex;                         \
++    printf '\\chapter{ML Functions in the {\\tt abs\\_theory} Library}' >entries.tex;   \
++    printf '\\input{entries-intro}' >>entries.tex;                         \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index:;                                                                 \
+--- a/Library/arith/Manual/Makefile
++++ b/Library/arith/Manual/Makefile
+@@ -26,16 +26,16 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the arith Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the arith Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index: 
+--- a/Library/finite_sets/Manual/Makefile
++++ b/Library/finite_sets/Manual/Makefile
+@@ -26,45 +26,45 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: theorems ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{The type definition}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{The type definition}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/sdef theorems.tex
+-	@echo "\section{Basic properties of {\tt EMPTY}, {\tt INSERT}, and {\tt IN}}">>theorems.tex
++	@printf '\\section{Basic properties of {\\tt EMPTY}, {\\tt INSERT}, and {\\tt IN}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/basic theorems.tex
+-	@echo "\section{Set inclusion}">>theorems.tex
++	@printf '\\section{Set inclusion}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/subs theorems.tex
+-	@echo "\section{Intersection and union}">>theorems.tex
++	@printf '\\section{Intersection and union}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/unin theorems.tex
+-	@echo "\section{Set difference}">>theorems.tex
++	@printf '\\section{Set difference}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/diff theorems.tex
+-	@echo "\section{Deletion of an element}">>theorems.tex
++	@printf '\\section{Deletion of an element}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/del theorems.tex
+-	@echo "\section{Disjoint sets}">>theorems.tex
++	@printf '\\section{Disjoint sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/disj theorems.tex
+-	@echo "\section{The {\tt CHOICE} and {\tt REST} functions}">>theorems.tex
++	@printf '\\section{The {\\tt CHOICE} and {\\tt REST} functions}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/chre theorems.tex
+-	@echo "\section{Image of a function on a set}">>theorems.tex
++	@printf '\\section{Image of a function on a set}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/image theorems.tex
+-	@echo "\section{Mappings between sets}">>theorems.tex
++	@printf '\\section{Mappings between sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/fun theorems.tex
+-	@echo "\section{Singleton sets}">>theorems.tex
++	@printf '\\section{Singleton sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/sing theorems.tex
+-	@echo "\section{Cardinality of sets}">>theorems.tex
++	@printf '\\section{Cardinality of sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/card theorems.tex
+ 
+ index: 
+--- a/Library/latex-hol/Manual/Makefile
++++ b/Library/latex-hol/Manual/Makefile
+@@ -28,16 +28,16 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids 
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the {\tt latex-hol} Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the {\\tt latex-hol} Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ 
+--- a/Library/more_arithmetic/Manual/Makefile
++++ b/Library/more_arithmetic/Manual/Makefile
+@@ -26,40 +26,40 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids theorems
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the more\_arithmetic Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the more\\_arithmetic Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}\label{thms}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{Theorems about Inequalities}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}\\label{thms}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{Theorems about Inequalities}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/ineq theorems.tex
+-	@echo "\section{Theorems about {\tt 0}}">>theorems.tex
++	@printf '\\section{Theorems about {\\tt 0}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/zero_ineq theorems.tex
+-	@echo "\section{Theorems about {\tt SUC}}">>theorems.tex
++	@printf '\\section{Theorems about {\\tt SUC}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/suc theorems.tex
+-	@echo "\section{Theorems about {\tt PRE}}">>theorems.tex
++	@printf '\\section{Theorems about {\\tt PRE}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/pre theorems.tex
+-	@echo "\section{Theorems about Addition}">>theorems.tex
++	@printf '\\section{Theorems about Addition}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/add theorems.tex
+-	@echo "\section{Theorems about Subtraction}">>theorems.tex
++	@printf '\\section{Theorems about Subtraction}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/sub theorems.tex
+-	@echo "\section{Theorems about Multiplication and Exponential Functions}">>theorems.tex
++	@printf '\\section{Theorems about Multiplication and Exponential Functions}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/mult theorems.tex
+-	@echo "\section{Theorems about Division}">>theorems.tex
++	@printf '\\section{Theorems about Division}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/div_mod theorems.tex
+-	@echo "\section{Theorems about Maximum and Minimum}">>theorems.tex
++	@printf '\\section{Theorems about Maximum and Minimum}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/min_max theorems.tex
+-	@echo "\section{Theorems about Odd and Even Numbers}">>theorems.tex
++	@printf '\\section{Theorems about Odd and Even Numbers}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/odd_even theorems.tex
+ 
+ index: 
+--- a/Library/numeral/Manual/Makefile
++++ b/Library/numeral/Manual/Makefile
+@@ -15,19 +15,19 @@
+ 
+ clean:;                                                                 \
+     rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex;              \
+-    echo "\begin{theindex}" >index.tex;                                 \
+-    echo "\mbox{}" >>index.tex;                                         \
+-    echo "\end{theindex}" >>index.tex
++    printf '\\begin{theindex}' >index.tex;                                 \
++    printf '\\mbox{}' >>index.tex;                                         \
++    printf '\\end{theindex}' >>index.tex
+ 
+ ids:;                                                                   \
+-    echo "\chapter{ML Functions in the numeral Library}" >entries.tex;  \
+-    echo "\input{entries-intro}" >>entries.tex;                         \
++    printf '\\chapter{ML Functions in the numeral Library}' >entries.tex;  \
++    printf '\\input{entries-intro}' >>entries.tex;                         \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ thms:;                                                                  \
+-    echo "\chapter{Pre-proved Theorems}" > theorems.tex;                \
+-    echo "\input{theorems-intro}" >> theorems.tex;                      \
+-    echo "\section{Numeral theory}" >> theorems.tex;                    \
++    printf '\\chapter{Pre-proved Theorems}' > theorems.tex;                \
++    printf '\\input{theorems-intro}' >> theorems.tex;                      \
++    printf '\\section{Numeral theory}' >> theorems.tex;                    \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/numeral theorems.tex
+ 
+ index:;                                                                 \
+--- a/Library/pair/Manual/Makefile
++++ b/Library/pair/Manual/Makefile
+@@ -26,19 +26,19 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex theorems.tex; \
+-	echo "\begin{theindex}" >index.tex;                                 \
+-	echo "\mbox{}" >>index.tex;                                         \
+-	echo "\end{theindex}" >>index.tex
++	printf '\\begin{theindex}' >index.tex;                                 \
++	printf '\\mbox{}' >>index.tex;                                         \
++	printf '\\end{theindex}' >>index.tex
+ 
+ ids:
+-	echo "\chapter{ML Functions in the pair Library}" >entries.tex;   	\
+-	echo "\input{entries-intro}" >>entries.tex;                         \
++	printf '\\chapter{ML Functions in the pair Library}' >entries.tex;   	\
++	printf '\\input{entries-intro}' >>entries.tex;                         \
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{Theorems}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{Theorems}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms theorems.tex
+ 
+ index:
+--- a/Library/parser/Manual/Makefile
++++ b/Library/parser/Manual/Makefile
+@@ -25,20 +25,20 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids theorems
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the parser Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the parser Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
+ 
+ index: 
+ 	${MAKEINDEX} parser.idx index.tex 
+--- a/Library/pred_sets/Manual/Makefile
++++ b/Library/pred_sets/Manual/Makefile
+@@ -25,47 +25,47 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: theorems ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{Membership, equality, and set specifications}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{Membership, equality, and set specifications}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/mem theorems.tex
+-	@echo "\section{The empty and universal sets}">>theorems.tex
++	@printf '\\section{The empty and universal sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/emuniv theorems.tex
+-	@echo "\section{Set inclusion}">>theorems.tex
++	@printf '\\section{Set inclusion}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/subs theorems.tex
+-	@echo "\section{Intersection and union}">>theorems.tex
++	@printf '\\section{Intersection and union}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/unin theorems.tex
+-	@echo "\section{Set difference}">>theorems.tex
++	@printf '\\section{Set difference}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/diff theorems.tex
+-	@echo "\section{Disjoint sets}">>theorems.tex
++	@printf '\\section{Disjoint sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/disj theorems.tex
+-	@echo "\section{Insertion and deletion of an element}">>theorems.tex
++	@printf '\\section{Insertion and deletion of an element}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/insdel theorems.tex
+-	@echo "\section{The {\tt CHOICE} and {\tt REST} functions}">>theorems.tex
++	@printf '\\section{The {\\tt CHOICE} and {\\tt REST} functions}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/chre theorems.tex
+-	@echo "\section{Image of a function on a set}">>theorems.tex
++	@printf '\\section{Image of a function on a set}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/image theorems.tex
+-	@echo "\section{Mappings between sets}">>theorems.tex
++	@printf '\\section{Mappings between sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/fun theorems.tex
+-	@echo "\section{Singleton sets}">>theorems.tex
++	@printf '\\section{Singleton sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/sing theorems.tex
+-	@echo "\section{Finite and infinite sets}">>theorems.tex
++	@printf '\\section{Finite and infinite sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/fin theorems.tex
+-	@echo "\section{Cardinality of sets}">>theorems.tex
++	@printf '\\section{Cardinality of sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/card theorems.tex
+ 
+ index: 
+--- a/Library/prettyp/Manual/Makefile
++++ b/Library/prettyp/Manual/Makefile
+@@ -26,16 +26,16 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the prettyp Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the prettyp Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index: 
+--- a/Library/reals/Manual/Makefile
++++ b/Library/reals/Manual/Makefile
+@@ -15,34 +15,34 @@
+ 
+ clean:;                                                                    \
+     rm -f *.dvi *.aux *.toc *.log *.idx *.ilg;                             \
+-    echo "\begin{theindex}" >index.tex;                                    \
+-    echo "\mbox{}" >>index.tex;                                            \
+-    echo "\end{theindex}" >>index.tex
++    printf '\\begin{theindex}' >index.tex;                                    \
++    printf '\\mbox{}' >>index.tex;                                            \
++    printf '\\end{theindex}' >>index.tex
+ 
+ tex: theorems
+ 
+ theorems:;                                                                 \
+-    echo "\chapter{Pre-proved Theorems}" >theorems.tex;                    \
+-    echo "\input{theorems-intro}" >>theorems.tex;                          \
+-    echo "\section{HRAT}" >>theorems.tex;                                  \
++    printf '\\chapter{Pre-proved Theorems}' >theorems.tex;                    \
++    printf '\\input{theorems-intro}' >>theorems.tex;                          \
++    printf '\\section{HRAT}' >>theorems.tex;                                  \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/HRAT theorems.tex;     \
+-    echo "\section{HREAL}" >>theorems.tex;                                 \
++    printf '\\section{HREAL}' >>theorems.tex;                                 \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/HREAL theorems.tex;    \
+-    echo "\section{REALAX}" >>theorems.tex;                                \
++    printf '\\section{REALAX}' >>theorems.tex;                                \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/REALAX theorems.tex;   \
+-    echo "\section{REAL}" >>theorems.tex;                                  \
++    printf '\\section{REAL}' >>theorems.tex;                                  \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/REAL theorems.tex;     \
+-    echo "\section{TOPOLOGY}" >>theorems.tex;                              \
++    printf '\\section{TOPOLOGY}' >>theorems.tex;                              \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/TOPOLOGY theorems.tex; \
+-    echo "\section{NETS}" >>theorems.tex;                                  \
++    printf '\\section{NETS}' >>theorems.tex;                                  \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/NETS theorems.tex;     \
+-    echo "\section{LIM}" >>theorems.tex;                                   \
++    printf '\\section{LIM}' >>theorems.tex;                                   \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/LIM theorems.tex;      \
+-    echo "\section{SEQ}" >>theorems.tex;                                   \
++    printf '\\section{SEQ}' >>theorems.tex;                                   \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/SEQ theorems.tex;      \
+-    echo "\section{POWSER}" >>theorems.tex;                                \
++    printf '\\section{POWSER}' >>theorems.tex;                                \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/POWSER theorems.tex;   \
+-    echo "\section{TRANSC}" >>theorems.tex;                                \
++    printf '\\section{TRANSC}' >>theorems.tex;                                \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/TRANSC theorems.tex
+ 
+ reals:;                                                                    \
+--- a/Library/record_proof/Manual/Makefile
++++ b/Library/record_proof/Manual/Makefile
+@@ -27,17 +27,17 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex:	 functions
+ 	@echo "TeX files made"
+ 
+ functions:
+-	@echo "\chapter{ML Functions in the {\tt record\_proof} Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the {\\tt record\\_proof} Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help} entries.tex
+ 
+ index: 
+--- a/Library/reduce/Manual/Makefile
++++ b/Library/reduce/Manual/Makefile
+@@ -15,13 +15,13 @@
+ 
+ clean:;                                                                 \
+     rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex;              \
+-    echo "\begin{theindex}" >index.tex;                                 \
+-    echo "\mbox{}" >>index.tex;                                         \
+-    echo "\end{theindex}" >>index.tex
++    printf '\\begin{theindex}' >index.tex;                                 \
++    printf '\\mbox{}' >>index.tex;                                         \
++    printf '\\end{theindex}' >>index.tex
+ 
+ ids:;                                                                   \
+-    echo "\chapter{ML Functions in the reduce Library}" >entries.tex;   \
+-    echo "\input{entries-intro}" >>entries.tex;                         \
++    printf '\\chapter{ML Functions in the reduce Library}' >entries.tex;   \
++    printf '\\input{entries-intro}' >>entries.tex;                         \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index:;                                                                 \
+--- a/Library/res_quan/Manual/Makefile
++++ b/Library/res_quan/Manual/Makefile
+@@ -27,22 +27,22 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: theorems functions
+ 	@echo "TeX files made"
+ 
+ functions:
+-	@echo "\chapter{ML Functions in the {\tt res\_quan} Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the {\\tt res\\_quan} Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms theorems.tex
+ 
+ index: 
+--- a/Library/sets/Manual/Makefile
++++ b/Library/sets/Manual/Makefile
+@@ -26,49 +26,49 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: theorems ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the sets Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the sets Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{The type definition}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{The type definition}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/sdef theorems.tex
+-	@echo "\section{Membership, equality, and set specifications}">>theorems.tex
++	@printf '\\section{Membership, equality, and set specifications}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/mem theorems.tex
+-	@echo "\section{The empty and universal sets}">>theorems.tex
++	@printf '\\section{The empty and universal sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/emuniv theorems.tex
+-	@echo "\section{Set inclusion}">>theorems.tex
++	@printf '\\section{Set inclusion}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/subs theorems.tex
+-	@echo "\section{Intersection and union}">>theorems.tex
++	@printf '\\section{Intersection and union}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/unin theorems.tex
+-	@echo "\section{Set difference}">>theorems.tex
++	@printf '\\section{Set difference}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/diff theorems.tex
+-	@echo "\section{Disjoint sets}">>theorems.tex
++	@printf '\\section{Disjoint sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/disj theorems.tex
+-	@echo "\section{Insertion and deletion of an element}">>theorems.tex
++	@printf '\\section{Insertion and deletion of an element}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/insdel theorems.tex
+-	@echo "\section{The {\tt CHOICE} and {\tt REST} functions}">>theorems.tex
++	@printf '\\section{The {\\tt CHOICE} and {\\tt REST} functions}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/chre theorems.tex
+-	@echo "\section{Image of a function on a set}">>theorems.tex
++	@printf '\\section{Image of a function on a set}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/image theorems.tex
+-	@echo "\section{Mappings between sets}">>theorems.tex
++	@printf '\\section{Mappings between sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/fun theorems.tex
+-	@echo "\section{Singleton sets}">>theorems.tex
++	@printf '\\section{Singleton sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/sing theorems.tex
+-	@echo "\section{Finite and infinite sets}">>theorems.tex
++	@printf '\\section{Finite and infinite sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/fin theorems.tex
+-	@echo "\section{Cardinality of sets}">>theorems.tex
++	@printf '\\section{Cardinality of sets}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/card theorems.tex
+ 
+ index: 
+--- a/Library/string/Manual/Makefile
++++ b/Library/string/Manual/Makefile
+@@ -26,24 +26,24 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids theorems
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the string Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the string Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{Definitions}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{Definitions}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/defs theorems.tex
+-	@echo "\section{Theorems}">>theorems.tex
++	@printf '\\section{Theorems}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms theorems.tex
+ 
+ index: 
+--- a/Library/taut/Manual/Makefile
++++ b/Library/taut/Manual/Makefile
+@@ -26,16 +26,16 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the taut Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the taut Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index: 
+--- a/Library/trs/Manual/Makefile
++++ b/Library/trs/Manual/Makefile
+@@ -26,16 +26,16 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the trs Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the trs Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index: 
+--- a/Library/unwind/Manual/Makefile
++++ b/Library/unwind/Manual/Makefile
+@@ -26,16 +26,16 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{ML Functions in the unwind Library}">entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the unwind Library}'>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ index: 
+--- a/Library/wellorder/Manual/Makefile
++++ b/Library/wellorder/Manual/Makefile
+@@ -14,26 +14,26 @@
+ 
+ clean:;                                                                 \
+     rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex;              \
+-    echo "\begin{theindex}" >index.tex;                                 \
+-    echo "\mbox{}" >>index.tex;                                         \
+-    echo "\end{theindex}" >>index.tex
++    printf '\\begin{theindex}' >index.tex;                                 \
++    printf '\\mbox{}' >>index.tex;                                         \
++    printf '\\end{theindex}' >>index.tex
+ 
+ tex: theorems ids
+ 
+ ids:;                                                                   \
+-    echo "\chapter{ML Functions in the wellorder Library}" >entries.tex;\
+-    echo "\label{entries}" >>entries.tex;                               \
+-    echo "\input{entries-intro}" >>entries.tex;                         \
++    printf '\\chapter{ML Functions in the wellorder Library}' >entries.tex;\
++    printf '\\label{entries}' >>entries.tex;                               \
++    printf '\\input{entries-intro}' >>entries.tex;                         \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:;                                                              \
+-    echo "\chapter{Pre-proved Theorems}" >theorems.tex;                 \
+-    echo "\input{theorems-intro}" >>theorems.tex;                       \
+-    echo "\section{Basic definitions}" >>theorems.tex;                  \
++    printf '\\chapter{Pre-proved Theorems}' >theorems.tex;                 \
++    printf '\\input{theorems-intro}' >>theorems.tex;                       \
++    printf '\\section{Basic definitions}' >>theorems.tex;                  \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/defs theorems.tex;  \
+-    echo "\section{Miscellaneous lemmas}" >>theorems.tex;               \
++    printf '\\section{Miscellaneous lemmas}' >>theorems.tex;               \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/lemmas theorems.tex;\
+-    echo "\section{Main theorems}"  >>theorems.tex;                     \
++    printf '\\section{Main theorems}'  >>theorems.tex;                     \
+     /bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/main theorems.tex
+ 
+ wellorder:;                                                             \
+--- a/Library/window/Manual/Makefile
++++ b/Library/window/Manual/Makefile
+@@ -26,24 +26,24 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex *.bak;        \
+-	echo "\begin{theindex}" >index.tex;                                 \
+-	echo "\mbox{}" >>index.tex;                                         \
+-	echo "\end{theindex}" >>index.tex
++	printf '\\begin{theindex}' >index.tex;                                 \
++	printf '\\mbox{}' >>index.tex;                                         \
++	printf '\\end{theindex}' >>index.tex
+ 
+ tex: ids theorems
+ 	@echo "TeX files makde"
+ 
+ ids:
+-	echo "\chapter{ML Functions in the window Library}" >entries.tex;   \
+-	echo "\input{entries-intro}" >>entries.tex;                         \
++	printf '\\chapter{ML Functions in the window Library}' >entries.tex;   \
++	printf '\\input{entries-intro}' >>entries.tex;                         \
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{Definitions}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{Definitions}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/defs theorems.tex
+-	@echo "\section{Theorems}">>theorems.tex
++	@printf '\\section{Theorems}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms theorems.tex
+ 
+ index:
+--- a/Library/word/Manual/Makefile
++++ b/Library/word/Manual/Makefile
+@@ -27,33 +27,33 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: theorems functions
+ 	@echo "TeX files made"
+ 
+ functions:
+-	@echo "\chapter{ML Functions in the {\tt word} Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the {\\tt word} Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/entries entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{The theory {\tt word\_base}}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{The theory {\\tt word\\_base}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/word_base theorems.tex
+-	@echo "\section{The theory {\tt word\_bitop}}">>theorems.tex
++	@printf '\\section{The theory {\\tt word\\_bitop}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/word_bitop theorems.tex
+-	@echo "\section{The theory {\tt word\_num}}">>theorems.tex
++	@printf '\\section{The theory {\\tt word\\_num}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/word_num theorems.tex
+-	@echo "\section{The theory {\tt bword\_bitop}}">>theorems.tex
++	@printf '\\section{The theory {\\tt bword\\_bitop}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/bword_bitop theorems.tex
+-	@echo "\section{The theory {\tt bword\_num}}">>theorems.tex
++	@printf '\\section{The theory {\\tt bword\\_num}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/bword_num theorems.tex
+-	@echo "\section{The theory {\tt bword\_arith}}">>theorems.tex
++	@printf '\\section{The theory {\\tt bword\\_arith}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/thms/bword_arith theorems.tex
+ 
+ index: 
+--- a/Manual/Reference/Makefile
++++ b/Manual/Reference/Makefile
+@@ -19,46 +19,46 @@
+ 
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex: ids theorems
+ 	@echo "TeX files made"
+ 
+ ids:
+-	@echo "\chapter{Pre-defined ML Identifiers}" > entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{Pre-defined ML Identifiers}' > entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/ENTRIES entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{Definitions of Basic Logical Constants}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{Definitions of Basic Logical Constants}'>>theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/basic-logic theorems.tex
+-	@echo "\section{Constants for syntactic abbreviations}" >> theorems.tex
++	@printf '\\section{Constants for syntactic abbreviations}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/syntax theorems.tex
+-	@echo "\section{Axioms}" >> theorems.tex
++	@printf '\\section{Axioms}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/axioms theorems.tex
+-	@echo "\section{Logical tautologies}" >> theorems.tex
++	@printf '\\section{Logical tautologies}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/logic theorems.tex
+-	@echo "\section{Theorems about functions}" >> theorems.tex
++	@printf '\\section{Theorems about functions}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/functions theorems.tex
+-	@echo "\section{Theorems about the type {\tt one}}" >> theorems.tex
++	@printf '\\section{Theorems about the type {\\tt one}}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/one theorems.tex
+-	@echo "\section{Theorems about combinators}" >> theorems.tex
++	@printf '\\section{Theorems about combinators}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/combin theorems.tex
+-	@echo "\section{Theorems about pairs}" >> theorems.tex
++	@printf '\\section{Theorems about pairs}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/pairs theorems.tex
+-	@echo "\section{Theorems about disjoint sums}" >> theorems.tex
++	@printf '\\section{Theorems about disjoint sums}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/sum theorems.tex
+-	@echo "\section{Theorems about arithmetic}" >> theorems.tex
++	@printf '\\section{Theorems about arithmetic}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/arith theorems.tex
+-	@echo "\section{Theorems about lists}" >> theorems.tex
++	@printf '\\section{Theorems about lists}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/list theorems.tex
+-	@echo "\section{Theorems about trees}" >> theorems.tex
++	@printf '\\section{Theorems about trees}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/tree theorems.tex
+-	@echo "\section{Theorems used to define types}" >> theorems.tex
++	@printf '\\section{Theorems used to define types}' >> theorems.tex
+ 	/bin/sh bin/doc-to-tex ${D2TSED} ${Helpd}/THEOREMS/tydefs theorems.tex
+ 
+ reference: 
+--- a/contrib/wordn/Manual/Makefile
++++ b/contrib/wordn/Manual/Makefile
+@@ -26,27 +26,27 @@
+ # ---------------------------------------------------------------------
+ clean:
+ 	rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
+-	@echo "\begin{theindex}" > index.tex
+-	@echo "\mbox{}" >> index.tex
+-	@echo "\end{theindex}" >> index.tex
++	@printf '\\begin{theindex}' > index.tex
++	@printf '\\mbox{}' >> index.tex
++	@printf '\\end{theindex}' >> index.tex
+ 
+ tex:	entries theorems
+ 	@echo "TeX files made"
+ 
+ entries:
+-	@echo "\chapter{ML Functions in the wordn Library}">entries.tex
+-	@echo "\label{entries}">>entries.tex
+-	@echo "\input{entries-intro}" >> entries.tex
++	@printf '\\chapter{ML Functions in the wordn Library}'>entries.tex
++	@printf '\\label{entries}'>>entries.tex
++	@printf '\\input{entries-intro}' >> entries.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/ENTRIES entries.tex
+ 
+ theorems:
+-	@echo "\chapter{Pre-proved Theorems}" > theorems.tex
+-	@echo "\input{theorems-intro}" >> theorems.tex
+-	@echo "\section{The theory {\tt wordn\_base}}">>theorems.tex
++	@printf '\\chapter{Pre-proved Theorems}' > theorems.tex
++	@printf '\\input{theorems-intro}' >> theorems.tex
++	@printf '\\section{The theory {\\tt wordn\\_base}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/THEOREMS/base theorems.tex
+-	@echo "\section{The theory {\tt wordn\_bitops}}">>theorems.tex
++	@printf '\\section{The theory {\\tt wordn\\_bitops}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/THEOREMS/bitops theorems.tex
+-	@echo "\section{The theory {\tt wordn\_num}}">>theorems.tex
++	@printf '\\section{The theory {\\tt wordn\\_num}}'>>theorems.tex
+ 	/bin/sh ${DOCTOTEX} ${DOCTOTEXSED} ${Help}/THEOREMS/num theorems.tex
+ 
+ index: 
--- hol88-2.02.19940316.orig/debian/copyright
+++ hol88-2.02.19940316/debian/copyright
@@ -0,0 +1,32 @@
+This package was debianized by Camm Maguire <camm@enhanced.com> on
+Wed, 18 Oct 2006 13:36:15 -0400.
+
+It was downloaded from http://www.ftp.cl.cam.ac.uk/ftp/hvg/hol88/
+
+Upstream Authors: Michael Gordon <Mike.Gordon@cl.cam.ac.uk>
+                  University of Cambridge Computer Laboratory http://www.cl.cam.ac.uk/                 
+
+Copyright: 1994 University of Edinburgh, University of Cambridge, INRIA
+
+License:
+
+public domain
+
+From http://www.cl.cam.ac.uk/~mjcg/papers/HolHistory.pdf:
+
+...
+
+6.1 HOL88
+
+The core HOL system became stable in about 1988. A new release that
+consolidated various changes and enhancements called HOL88 was issued
+then.11 We were fortunate to receive support from DSTO Australia to
+document HOL12 and from Hewlett Packard to port it from Franz Lisp to
+Common Lisp (a job very ably done by John Carroll). The current
+versions of HOL and its documentation are public domain13 and
+available on the Internet
+(http://lal.cs.byu.edu/lal/hol-documentation.html).
+
+
+The Debian packaging is (C) 2006, Camm Maguire <camm@enhanced.com> and
+is licensed under the GPL, see `/usr/share/common-licenses/GPL'.
--- hol88-2.02.19940316.orig/debian/site_ml_orig
+++ hol88-2.02.19940316/debian/site_ml_orig
@@ -0,0 +1,34 @@
+%=============================================================================%
+%                                    HOL 88                                   %
+%                                                                             %
+%     FILE NAME:        site.ml.orig                                          %
+%                                                                             %
+%     DESCRIPTION:      Source file for site dependent information            %
+%                                                                             %
+%     USES FILES:       hol-lcf lisp files                                    %
+%                                                                             %
+%                       University of Cambridge                               %
+%                       Hardware Verification Group                           %
+%                       Computer Laboratory                                   %
+%                       New Museums Site                                      %
+%                       Pembroke Street                                       %
+%                       Cambridge  CB2 3QG                                    %
+%                       England                                               %
+%                                                                             %
+%     COPYRIGHT:        University of Edinburgh                               %
+%     COPYRIGHT:        University of Cambridge                               %
+%     COPYRIGHT:        INRIA                                                 %
+%                                                                             %
+%     VERSION:          2.0                                                   %
+%     REVISION HISTORY: 91.02.24 TFM                                          %
+%=============================================================================%
+
+% Must be compiled when other ml sources are compiled %
+
+let concat tok1 tok2 = implode( explode tok1 @ explode tok2);;
+
+let ml_dir_pathname = `ml/`;;
+let lisp_dir_pathname = `lisp/`;;
+
+% No longer needed.		  [TFM 91.02.24] %
+% let theories_dir_pathname = `theories/`;;      %
--- hol88-2.02.19940316.orig/debian/dirs
+++ hol88-2.02.19940316/debian/dirs
@@ -0,0 +1 @@
+usr/bin
--- hol88-2.02.19940316.orig/debian/README.Debian
+++ hol88-2.02.19940316/debian/README.Debian
@@ -0,0 +1,10 @@
+hol88 for Debian
+----------------
+
+This package is built from the last lisp sources to the HOL theorem
+proving system.  More recent versions are written purely in ML.  This
+package is being provided here as a facility to combine ML and lisp
+into one image, as well as to provide an instructive example in one of
+the major milestones in the history of automated theorem proving.
+
+ -- Camm Maguire <camm@enhanced.com>, Wed, 18 Oct 2006 13:51:08 -0400
--- hol88-2.02.19940316.orig/debian/changelog
+++ hol88-2.02.19940316/debian/changelog
@@ -0,0 +1,114 @@
+hol88 (2.02.19940316-14) unstable; urgency=low
+
+  * rebuild against latest gcl
+
+ -- Camm Maguire <camm@debian.org>  Tue, 17 May 2011 15:01:32 +0000
+
+hol88 (2.02.19940316-13.1) unstable; urgency=high
+
+  * Non-maintainer upload.
+  * Revert build-depend bump, as that version of gcl will
+    not make it into Squeeze (Closes: #606293)
+
+ -- Jonathan Wiltshire <jmw@debian.org>  Tue, 14 Dec 2010 20:47:42 +0000
+
+hol88 (2.02.19940316-13) unstable; urgency=low
+
+  * build depend on latest gcl
+
+ -- Camm Maguire <camm@debian.org>  Fri, 05 Nov 2010 16:09:55 +0000
+
+hol88 (2.02.19940316-12) unstable; urgency=low
+
+  * remove stray raw_*_map files
+
+ -- Camm Maguire <camm@debian.org>  Thu, 21 Oct 2010 19:59:51 +0000
+
+hol88 (2.02.19940316-11) unstable; urgency=low
+
+  * build-dep on latest gcl
+  * Bug fix: "[mips] empty package", thanks to Jakub Wilk (Closes:
+    #597140).
+  * Bug fix: "FTBFS on mipsel: Unrecoverable error: Segmentation
+    violation..", thanks to Cyril Brulebois (Closes: #599986).
+  * Bug fix: "FTBFS on hppa: /bin/sh: ././raw_hol_map: Permission denied",
+    thanks to Cyril Brulebois (Closes: #599987).
+
+ -- Camm Maguire <camm@debian.org>  Thu, 21 Oct 2010 14:34:13 +0000
+
+hol88 (2.02.19940316-10) unstable; urgency=low
+
+  * rebuild against newest gcl
+
+ -- Camm Maguire <camm@debian.org>  Sat, 25 Sep 2010 15:19:33 +0000
+
+hol88 (2.02.19940316-9) unstable; urgency=low
+
+  * Bug fix: "replacing libreadline5-dev build dependency with
+    libreadline-dev", thanks to Matthias Klose (Closes: #553782).
+  * Bug fix: "hol88 crashes with segfault", thanks to Benedikt Ahrens
+    (Closes: #508908).
+
+ -- Camm Maguire <camm@debian.org>  Sun, 03 Jan 2010 20:48:22 +0000
+
+hol88 (2.02.19940316-8) unstable; urgency=low
+
+  * Bug fix: "FTBFS: LaTeX Error: \begin{document} ended by
+    \end{theindex}", thanks to Chris Lamb (Closes: #484983).
+  * Bug fix: "hol88: bashism in debian/rules", thanks to Raphael Geissert
+    (Closes: #477583).
+
+ -- Camm Maguire <camm@sacrifice.m.enhanced.com>  Sat, 02 Aug 2008 13:23:41 +0000
+
+hol88 (2.02.19940316-7) unstable; urgency=low
+
+  * Bug fix: "hol88: empty package on arm", thanks to Niko Tyni (Closes:
+    #448843). Rebuild against latest gcl
+
+ -- Camm Maguire <camm@enhanced.com>  Mon, 03 Dec 2007 09:18:22 -0500
+
+hol88 (2.02.19940316-6) unstable; urgency=low
+
+  * build-depend on texlive-latex-base
+  * Bug fix: "hol88: package content changed if build twice or more times
+    in a row", thanks to Patrick Winnertz (Closes: #441710). preserve
+    debian/site_ml_orig
+  * Bug fix: "hol88: dangling symlinks", thanks to Ian Zimmerman (Closes:
+    #442282). write absolute paths in first entry in links files
+
+ -- Camm Maguire <camm@enhanced.com>  Wed, 24 Oct 2007 14:01:30 -0400
+
+hol88 (2.02.19940316-5) unstable; urgency=low
+
+  * Fix patch mechanism for non native relocs
+
+ -- Camm Maguire <camm@enhanced.com>  Mon,  4 Dec 2006 10:39:08 -0500
+
+hol88 (2.02.19940316-4) unstable; urgency=low
+
+  * Proper build deps for non-native-reloc arches
+
+ -- Camm Maguire <camm@enhanced.com>  Sat,  2 Dec 2006 23:28:42 -0500
+
+hol88 (2.02.19940316-3) unstable; urgency=low
+
+  * Fix native-reloc target, Closes: #401321
+
+ -- Camm Maguire <camm@enhanced.com>  Sat,  2 Dec 2006 17:58:39 -0500
+
+hol88 (2.02.19940316-2) unstable; urgency=low
+
+  * redefine ml-save to use si::save-system, and si::*top-level-hook*.
+    Fixes amd64 and sparc builds
+  * patch Makefile and make-user-init function (from gcl cvs head) to
+    support build on systems without native object relocation. Closes:
+    #400063.
+
+ -- Camm Maguire <camm@enhanced.com>  Tue, 28 Nov 2006 16:30:04 -0500
+
+hol88 (2.02.19940316-1) unstable; urgency=low
+
+  * Initial release
+
+ -- Camm Maguire <camm@enhanced.com>  Wed, 18 Oct 2006 13:36:15 -0400
+
--- hol88-2.02.19940316.orig/debian/gcl_save.l
+++ hol88-2.02.19940316/debian/gcl_save.l
@@ -0,0 +1 @@
+(si::save-system "gcl")
--- hol88-2.02.19940316.orig/debian/hol88-doc.docs
+++ hol88-2.02.19940316/debian/hol88-doc.docs
@@ -0,0 +1,2 @@
+#DOCS#
+
--- hol88-2.02.19940316.orig/lisp/f-cl.l
+++ hol88-2.02.19940316/lisp/f-cl.l
@@ -164,10 +164,11 @@
          :gc t)
       #+kcl
       (progn
-         (setf (symbol-function 'si:top-level)
-            `(lambda nil (tml)))
+;         (setf (symbol-function 'si:top-level)
+;            `(lambda nil (tml)))
+	 (setq si::*top-level-hook* (lambda nil (tml)))
          (gbc t)
-         (save file))
+         (si::save-system file))
       #+allegro
       (progn
          (setf (symbol-function 'excl::copyright-banner)
@@ -569,10 +570,19 @@
       (setq *standard-input* (pop inputstack))
       (close current-input)))
 
+(defconstant +fast-digits+ 4)
+(defconstant +slow-digits+ (- (truncate (log most-positive-fixnum 10) 1.0) +fast-digits+))
+(defconstant +fast-mod+ (expt 10 +fast-digits+))
+(defconstant +slow-mod+ (expt 10 +slow-digits+))
+
 
 (defun clock ()
    ;; Get absolute time - just for time-stamps
-   (get-universal-time))
+  (let ((s (get-universal-time))
+	(m (si::gettimeofday)))
+    (+ (* +fast-mod+ (mod s +slow-mod+))
+       (mod (truncate (* +fast-mod+ m) 1.0) +fast-mod+))))
+; (get-universal-time))
 
 
 ;;; Add extension .o to a file name for output name in process of
--- hol88-2.02.19940316.orig/lisp/f-iox-stand.l
+++ hol88-2.02.19940316/lisp/f-iox-stand.l
@@ -283,7 +283,7 @@
 
 (defun find-file1 (dir name exts)
    (do
-      ((exts exts (cdr exts))
+      ((exts (cons "" exts) (cdr exts))
          (file nil))
       ((null exts) nil)
       (setq file (catenate dir name (car exts)))
--- hol88-2.02.19940316.orig/lisp/f-format.l
+++ hol88-2.02.19940316/lisp/f-format.l
@@ -131,8 +131,8 @@
 (defun flush-output-buffer nil
    ;; Some data types (e.g. streams) cannot be catenated in franz, so
    ;; print out items in buffer separately. 
-   #+franz (mapc #'llprinc (nreverse %output-buffer))
-   #-franz (llprinc (apply #'catenate (nreverse %output-buffer)))
+   #+(or franz gcl) (mapc #'llprinc (nreverse %output-buffer))
+   #-(or franz gcl) (llprinc (apply #'catenate (nreverse %output-buffer)))
    (setq %output-buffer nil))
 
 
--- hol88-2.02.19940316.orig/Manual/Makefile
+++ hol88-2.02.19940316/Manual/Makefile
@@ -41,3 +41,5 @@
 	make tutorial;make description; make reference;make libraries;make covers
 	@echo "=======> MANUAL made"
 
+clean:
+	for i in Tutorial Description Reference Libraries Covers ; do $(MAKE) -C $$i clean ; done
--- hol88-2.02.19940316.orig/Manual/Reference/entries.tex
+++ hol88-2.02.19940316/Manual/Reference/entries.tex
@@ -1,1114 +1,882 @@
-\chapter{Pre-defined ML Identifiers}
-\input{entries-intro}
-\DOC{\#}
+\chapter{Pre-defined ML Identifiers}\input{entries-intro}\DOC{ABS\_CONV}
 
-\TYPE {\small\verb%$# : (((* -> **) # (*** -> ****)) -> (* # ***) -> (** # ****))%}\egroup
+\TYPE {\small\verb%ABS_CONV : (conv -> conv)%}\egroup
 
 \SYNOPSIS
-Applies two functions to a pair: {\small\verb%(f # g) (x,y)%} = {\small\verb%(f x, g y)%}.
+Applies a conversion to the body of an abstraction.
+
+\DESCRIBE
+If {\small\verb%c%} is a conversion that maps a term {\small\verb%"t"%} to the theorem {\small\verb%|- t = t'%}, then
+the conversion {\small\verb%ABS_CONV c%} maps abstractions of the form {\small\verb%"\x.t"%} to theorems
+of the form:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- (\x.t) = (\x.t')
+\end{verbatim}
+}
+\noindent That is, {\small\verb%ABS_CONV c "\x.t"%} applies {\small\verb%c%} to the body of the
+abstraction {\small\verb%"\x.t"%}.
 
 \FAILURE
-Never fails.
+{\small\verb%ABS_CONV c tm%} fails if {\small\verb%tm%} is not an abstraction or if {\small\verb%tm%} has the form
+{\small\verb%"\x.t"%} but the conversion {\small\verb%c%} fails when applied to the term {\small\verb%t%}. The
+function returned by {\small\verb%ABS_CONV c%} may also fail if the ML function
+{\small\verb%c:term->thm%} is not, in fact, a conversion (i.e. a function that maps a term
+{\small\verb%t%} to a theorem {\small\verb%|- t = t'%}).
 
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#ABS_CONV SYM_CONV "\x. 1 = x";;
+|- (\x. 1 = x) = (\x. x = 1)
+\end{verbatim}
+}
 \SEEALSO
-B, C, CB, Co, I, K, KI, o, oo, S, W.
+RAND_CONV, RATOR_CONV, SUB_CONV.
 
 \ENDDOC
-\DOC{*}
+\DOC{ABS}
 
-\TYPE {\small\verb%$* : ((int # int) -> int)%}\egroup
+\TYPE {\small\verb%ABS : (term -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Performs multiplication on ML integers.
+Abstracts both sides of an equation.
 
+\DESCRIBE
+{\par\samepage\setseps\small
+\begin{verbatim}
+         A |- t1 = t2
+   ------------------------  ABS "x"            [Where x is not free in A]
+    A |- (\x.t1) = (\x.t2)
+\end{verbatim}
+}
 \FAILURE
-Never fails.
+If the theorem is not an equation, or if the variable {\small\verb%x%} is free in the
+assumptions {\small\verb%A%}.
 
-\ENDDOC
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#ABS "m:num" (REFL "m:num");;
+|- (\m. m) = (\m. m)
+\end{verbatim}
+}
+\SEEALSO
+ETA_CONV, EXT, MK_ABS.
 
-\DOC{+}
+\ENDDOC
+\DOC{abs\_goals}
 
-\TYPE {\small\verb%$+ : ((int # int) -> int)%}\egroup
+\TYPE {\small\verb%abs_goals : (subgoals list -> goalstack)%}\egroup
 
 \SYNOPSIS
-Performs addition on ML integers.
-
-\FAILURE
-Never fails.
+This function is for internal use only and is to be deleted from a future
+version of the system. It should not be used.
 
 \ENDDOC
-\DOC{-}
+\DOC{ACCEPT\_TAC}
 
-\TYPE {\small\verb%$- : ((int # int) -> int)%}\egroup
+\TYPE {\small\verb%ACCEPT_TAC : thm_tactic%}\egroup
 
 \SYNOPSIS
-Performs subtraction on ML integers.
+Solves a goal if supplied with the desired theorem (up to alpha-conversion).
+
+\DESCRIBE
+{\small\verb%ACCEPT_TAC%} maps a given theorem {\small\verb%th%} to a tactic that solves any goal whose
+conclusion is alpha-convertible to the conclusion of {\small\verb%th%}.
 
 \FAILURE
-Never fails.
+{\small\verb%ACCEPT_TAC th (A,g)%} fails if the term {\small\verb%g%} is not alpha-convertible to the
+conclusion of the supplied theorem {\small\verb%th%}.
 
-\COMMENTS
-Unary {\small\verb%-%} exists as an internal parser object, but not as a function.  So,
-whilst typing in {\small\verb%-1;;%} will work, {\small\verb%-;;%} will return a parse error.
+\EXAMPLE
+{\small\verb%ACCEPT_TAC%} applied to the axiom
+{\par\samepage\setseps\small
+\begin{verbatim}
+   BOOL_CASES_AX = |- !t. (t = T) \/ (t = F)
+\end{verbatim}
+}
+\noindent will solve the goal
+{\par\samepage\setseps\small
+\begin{verbatim}
+   ?- !x. (x = T) \/ (x = F)
+\end{verbatim}
+}
+\noindent but will fail on the goal
+{\par\samepage\setseps\small
+\begin{verbatim}
+   ?- !x. (x = F) \/ (x = T)
+\end{verbatim}
+}
+\USES
+Used for completing proofs by supplying an existing theorem, such as an axiom,
+or a lemma already proved.
+
+\SEEALSO
+MATCH_ACCEPT_TAC.
 
 \ENDDOC
-\DOC{\char'056}
+\DOC{AC\_CONV}
 
-\TYPE {\small\verb%$. : ((* # * list) -> * list)%}\egroup
+\TYPE {\small\verb%AC_CONV : ((thm # thm) -> conv)%}\egroup
 
 \SYNOPSIS
-Adds single element to the head of a list.
+Proves equality of terms using associative and commutative laws.
 
 \DESCRIBE
-The {\small\verb%.%} operator is an infixed primitive list constructor, analogous to {\small\verb%CONS%}
-in LISP. Its effect is {\small\verb%x . [x1;....;xn]%} = {\small\verb%[x;x1;...;xn]%}.
+Suppose {\small\verb%_%} is a function, which is assumed to be infix in the following syntax,
+and {\small\verb%ath%} and {\small\verb%cth%} are theorems expressing its associativity and
+commutativity; they must be of the following form, except that any free
+variables may have arbitrary names and may be universally quantified:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   ath = |- m _ (n _ p) = (m _ n) _ p
+   cth = |- m _ n = n _ m
+\end{verbatim}
+}
+\noindent Then the conversion {\small\verb%AC_CONV(ath,cth)%} will prove equations whose
+left and right sides can be made identical using these associative and
+commutative laws.
 
 \FAILURE
-Never fails.
+Fails if the associative or commutative law has an invalid form, or if the
+term is not an equation between AC-equivalent terms.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #AC_CONV(ADD_ASSOC,ADD_SYM)
+   #  "x + (SUC t) + ((3 + y) + z) = 3 + (SUC t) + x + y + z";;
+   |- (x + ((SUC t) + ((3 + y) + z)) = 3 + ((SUC t) + (x + (y + z)))) = T
+\end{verbatim}
+}
+
+\COMMENTS
+Note that the preproved associative and commutative laws for the operators {\small\verb%+%},
+{\small\verb%*%}, {\small\verb%/\%} and {\small\verb%\/%} are already in the right form to give to {\small\verb%AC_CONV%}.
+
+\SEEALSO
+SYM_CONV.
 
 \ENDDOC
-\DOC{/}
+\DOC{achieve\_first}
 
-\TYPE {\small\verb%$/ : ((int # int) -> int)%}\egroup
+\TYPE {\small\verb%achieve_first : (subgoals -> thm -> subgoals)%}\egroup
 
 \SYNOPSIS
-Performs division on ML integers.
+This function is for internal use only and is to be deleted from a future
+version of the system. It should not be used.
 
-\FAILURE
-Fails on division by zero.
+\ENDDOC
+\DOC{achieves}
+
+\TYPE {\small\verb%achieves : (thm -> goal -> bool)%}\egroup
+
+\SYNOPSIS
+This function is for internal use only and is to be deleted from a future
+version of the system. It should not be used.
 
 \ENDDOC
-\DOC{\char'136}
+\DOC{aconv}
 
-\TYPE {\small\verb%$^ : (string -> string -> string)%}\egroup
+\TYPE {\small\verb%aconv : (term -> term -> bool)%}\egroup
 
 \SYNOPSIS
-Concatenates two ML strings.
+Tests for alpha-convertibility of terms.
 
 \DESCRIBE
-The {\small\verb%^%} is the ML infix string concatenation operator.
-If {\small\verb%s1%} and {\small\verb%s2%} are strings, then {\small\verb%s1^s2%} gives a string which is their
-concatenation.
+When applied to two terms, {\small\verb%aconv%} returns {\small\verb%true%} if they are
+alpha-convertible, and {\small\verb%false%} otherwise.
 
 \FAILURE
 Never fails.
 
 \EXAMPLE
+A simple case of alpha-convertibility is the renaming of a single quantified
+variable:
 {\par\samepage\setseps\small
 \begin{verbatim}
-#`Hello `^`world`;;
-`Hello world` : string
+   #aconv "?x. x=T" "?y. y=T";;
+   true : bool
 \end{verbatim}
 }
-\COMMENTS
-The ML role of the {\small\verb%^%} operator should not be confused with its use in
-quoted terms to introduce antiquotation (see DESCRIPTION for details).
-
 \SEEALSO
-concat, concatl.
+ALPHA, ALPHA_CONV.
 
 \ENDDOC
-\DOC{<}
+\DOC{activate\_binders}
 
-\TYPE {\small\verb%$< : ((int # int) -> bool)%}\egroup
+\TYPE {\small\verb%activate_binders : (string -> string list)%}\egroup
 
 \SYNOPSIS
-Performs a less-than test on ML integers.
+Makes the quotation parser treat all binders in the current theory segment as
+such.
+
+\DESCRIBE
+The call
+{\par\samepage\setseps\small
+\begin{verbatim}
+   activate_binders `thy`
+\end{verbatim}
+}
+\noindent where {\small\verb%thy%} is an ancestor theory ({\small\verb%`-`%} stands for the current
+theory), will return a list of all binders on that theory, and make the parser
+treat them all as binders, that is, for each binder {\small\verb%b%}, will allow the
+syntactic sugaring {\small\verb%"b x. y"%} as a shorthand for {\small\verb%"b (\x. y)"%}. The special
+syntactic status may be suppressed by preceding {\small\verb%b%} with a dollar sign. The
+function returns a list of all the binders dealt with.
 
 \FAILURE
 Never fails.
 
+\COMMENTS
+This function is mainly intended for internal use. All binders declared by
+{\small\verb%new_binder%} or {\small\verb%new_binder_definition%} are always parsed as such anyway.
+
+\SEEALSO
+activate_all_binders, binders, new_binder, parse_as_binder.
+
 \ENDDOC
-\DOC{<<}
+\DOC{ADD\_ASSUM}
 
-\TYPE {\small\verb%$<< : ((* # **) -> bool)%}\egroup
+\TYPE {\small\verb%ADD_ASSUM : (term -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Performs a lexical comparison of values.
+Adds an assumption to a theorem.
 
 \DESCRIBE
-{\small\verb%$<<%} performs a fast ordering on values.  It is substitutive with
-respect to equality in ML (i.e. if {\small\verb%x << y%} and {\small\verb%x = x'%} and {\small\verb%y = y'%}
-then {\small\verb%x' << y'%}).
+When applied to a boolean term {\small\verb%s%} and a theorem {\small\verb%A |- t%}, the inference
+rule {\small\verb%ADD_ASSUM%} returns the theorem {\small\verb%A u {s} |- t%}.
+{\par\samepage\setseps\small
+\begin{verbatim}
+       A |- t
+   --------------  ADD_ASSUM "s"
+    A u {s} |- t
+\end{verbatim}
+}
+\noindent {\small\verb%ADD_ASSUM%} performs straightforward set union with the new
+assumption; it checks for identical assumptions, but not for alpha-equivalent
+ones. The position at which the new assumption is inserted into the assumption
+list should not be relied on.
 
 \FAILURE
-Never fails.
-
-\USES
-It is often useful, for example in normalizing terms in some way, to be able to
-impose some arbitrary (but definite) ordering on ML values.
+Fails unless the given term has type {\small\verb%bool%}.
 
 \SEEALSO
-=.
+ASSUME, UNDISCH.
 
 \ENDDOC
-\DOC{=}
+\DOC{ADD\_CONV}
 
-\TYPE {\small\verb%$= : ((* # *) -> bool)%}\egroup
+\TYPE {\small\verb%ADD_CONV : conv%}\egroup
 
 \SYNOPSIS
-Performs an equality test on two ML values.
+Computes the sum of two natural number constants.
 
 \DESCRIBE
-{\small\verb%$=%} works as expected on non-function types.  It may give unexpected results
-when applied to function types (or types containing them, such as a pair of
-functions), and should be considered unreliable in those situations.
+If {\small\verb%n%} and {\small\verb%m%} are numeral constants (e.g. {\small\verb%0%}, {\small\verb%1%}, {\small\verb%2%}, {\small\verb%3%},...), then
+{\small\verb%ADD_CONV "n + m"%} returns the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- n + m = s
+\end{verbatim}
+}
+\noindent where {\small\verb%s%} is the numeral that denotes the sum of the natural
+numbers denoted by {\small\verb%n%} and {\small\verb%m%}.
 
 \FAILURE
-Never fails.
+{\small\verb%ADD_CONV tm%} fails if {\small\verb%tm%} is not of the form  {\small\verb%"n + m"%}, where {\small\verb%n%} and
+{\small\verb%m%} are numerals.
 
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#1 = 2;;
-false : bool
-
-#1 = 1;;
-true : bool
-
-#let f x = x + 1 and g x = x + 2;;
-f = - : (int -> int)
-g = - : (int -> int)
-
-#let f' = f and h x = f x and h' x = x + 1;;
-f' = - : (int -> int)
-h = - : (int -> int)
-h' = - : (int -> int)
-
-#f=f;;
-true : bool
-
-#f = f';;
-true : bool
-
-#f = g;;
-false : bool
-
-#f =h;;
-false : bool
-
-#f=h';;
-false : bool
-
-#h = h';;
-false : bool
+#ADD_CONV "75 + 25";;
+|- 75 + 25 = 100
 \end{verbatim}
 }
 \ENDDOC
-\DOC{>}
-
-\TYPE {\small\verb%$> : ((int # int) -> bool)%}\egroup
-
-\SYNOPSIS
-Performs a greater-than test on ML integers.
-
-\FAILURE
-Never fails.
-
-\ENDDOC
-\DOC{\char'100}
+\DOC{ALL\_CONV}
 
-\TYPE {\small\verb%$@ : ((* list # * list) -> * list)%}\egroup
+\TYPE {\small\verb%ALL_CONV : conv%}\egroup
 
 \SYNOPSIS
-Concatenates two lists.
+Conversion that always succeeds and leaves a term unchanged.
 
 \DESCRIBE
-{\small\verb%@%} is an infix operator which concatenates two lists.
+When applied to a term {\small\verb%"t"%}, the conversion {\small\verb%ALL_CONV%} returns the
+theorem {\small\verb%|- t = t%}.
 
 \FAILURE
 Never fails.
 
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#[1;2;3] @ [4;5;6];;
-[1; 2; 3; 4; 5; 6] : int list
-\end{verbatim}
-}
+\USES
+Identity element for {\small\verb%THENC%}.
+
 \SEEALSO
-append.
+NO_CONV, REFL.
 
 \ENDDOC
-\DOC{ABS}
+\DOC{ALL\_EL\_CONV}
 
-\TYPE {\small\verb%ABS : (term -> thm -> thm)%}\egroup
+\TYPE {\small\verb%ALL_EL_CONV : conv -> conv%}\egroup
 
 \SYNOPSIS
-Abstracts both sides of an equation.
+Computes by inference the result of applying a predicate to elements of a list.
 
 \DESCRIBE
+{\small\verb%ALL_EL_CONV%} takes a conversion {\small\verb%conv%} and a term {\small\verb%tm%} in the following form:
 {\par\samepage\setseps\small
 \begin{verbatim}
-         A |- t1 = t2
-   ------------------------  ABS "x"            [Where x is not free in A]
-    A |- (\x.t1) = (\x.t2)
-\end{verbatim}
-}
-\FAILURE
-If the theorem is not an equation, or if the variable {\small\verb%x%} is free in the
-assumptions {\small\verb%A%}.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#ABS "m:num" (REFL "m:num");;
-|- (\m. m) = (\m. m)
+   ALL_EL P [x0;...xn]
 \end{verbatim}
 }
-\SEEALSO
-ETA_CONV, EXT, MK_ABS.
-
-\ENDDOC
-\DOC{ABS\_CONV}
-
-\TYPE {\small\verb%ABS_CONV : (conv -> conv)%}\egroup
-
-\SYNOPSIS
-Applies a conversion to the body of an abstraction.
-
-\DESCRIBE
-If {\small\verb%c%} is a conversion that maps a term {\small\verb%"t"%} to the theorem {\small\verb%|- t = t'%}, then
-the conversion {\small\verb%ABS_CONV c%} maps abstractions of the form {\small\verb%"\x.t"%} to theorems
-of the form:
+\noindent It returns the theorem
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (\x.t) = (\x.t')
+   |- ALL_EL P [x0;...xn] = T
 \end{verbatim}
 }
-\noindent That is, {\small\verb%ABS_CONV c "\x.t"%} applies {\small\verb%c%} to the body of the
-abstraction {\small\verb%"\x.t"%}.
-
-\FAILURE
-{\small\verb%ABS_CONV c tm%} fails if {\small\verb%tm%} is not an abstraction or if {\small\verb%tm%} has the form
-{\small\verb%"\x.t"%} but the conversion {\small\verb%c%} fails when applied to the term {\small\verb%t%}. The
-function returned by {\small\verb%ABS_CONV c%} may also fail if the ML function
-{\small\verb%c:term->thm%} is not, in fact, a conversion (i.e. a function that maps a term
-{\small\verb%t%} to a theorem {\small\verb%|- t = t'%}).
-
-\EXAMPLE
+\noindent if for every {\small\verb%xi%} occurred in the list, {\small\verb%conv "P xi"%} returns a theorem {\small\verb%|- P xi = T%}, otherwise, if for at least one {\small\verb%xi%}, evaluating 
+{\small\verb%conv "P xi"%} returns the theorem {\small\verb%|- P xi = F%}, then it returns the theorem
 {\par\samepage\setseps\small
 \begin{verbatim}
-#ABS_CONV SYM_CONV "\x. 1 = x";;
-|- (\x. 1 = x) = (\x. x = 1)
+   |- ALL_EL P [x0;...xn] = F
 \end{verbatim}
 }
-\SEEALSO
-RAND_CONV, RATOR_CONV, SUB_CONV.
-
-\ENDDOC
-\DOC{abs\_goals}
-
-\TYPE {\small\verb%abs_goals : (subgoals list -> goalstack)%}\egroup
-
-\SYNOPSIS
-This function is for internal use only and is to be deleted from a future
-version of the system. It should not be used.
-
-\ENDDOC
-\DOC{ACCEPT\_TAC}
-
-\TYPE {\small\verb%ACCEPT_TAC : thm_tactic%}\egroup
-
-\SYNOPSIS
-Solves a goal if supplied with the desired theorem (up to alpha-conversion).
-
-\DESCRIBE
-{\small\verb%ACCEPT_TAC%} maps a given theorem {\small\verb%th%} to a tactic that solves any goal whose
-conclusion is alpha-convertible to the conclusion of {\small\verb%th%}.
 
 \FAILURE
-{\small\verb%ACCEPT_TAC th (A,g)%} fails if the term {\small\verb%g%} is not alpha-convertible to the
-conclusion of the supplied theorem {\small\verb%th%}.
+{\small\verb%ALL_EL_CONV conv tm%} fails if {\small\verb%tm%} is not of the form described above, or
+failure occurs when evaluating {\small\verb%conv "P xi"%} for some {\small\verb%xi%}.
 
 \EXAMPLE
-{\small\verb%ACCEPT_TAC%} applied to the axiom
+Evaluating
 {\par\samepage\setseps\small
 \begin{verbatim}
-   BOOL_CASES_AX = |- !t. (t = T) \/ (t = F)
+   ALL_EL_CONV bool_EQ_CONV "ALL_EL ($= T) [T;F;T]";;
 \end{verbatim}
 }
-\noindent will solve the goal
+\noindent returns the following theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   ?- !x. (x = T) \/ (x = F)
+   |- ALL_EL($= T)[T;F;T] = F
 \end{verbatim}
 }
-\noindent but will fail on the goal
+\noindent   In general, if the predicate {\small\verb%P%} is an explicit lambda abstraction
+{\small\verb%(\x. P x)%}, the conversion should be in the form
 {\par\samepage\setseps\small
 \begin{verbatim}
-   ?- !x. (x = F) \/ (x = T)
+   (BETA_CONV THENC conv')
 \end{verbatim}
 }
-\USES
-Used for completing proofs by supplying an existing theorem, such as an axiom,
-or a lemma already proved.
 
 \SEEALSO
-MATCH_ACCEPT_TAC.
-
-\ENDDOC
-\DOC{achieves}
-
-\TYPE {\small\verb%achieves : (thm -> goal -> bool)%}\egroup
-
-\SYNOPSIS
-This function is for internal use only and is to be deleted from a future
-version of the system. It should not be used.
+SOME_EL_CONV, IS_EL_CONV, FOLDL_CONV, FOLDR_CONV, list_FOLD_CONV.
 
 \ENDDOC
-\DOC{achieve\_first}
-
-\TYPE {\small\verb%achieve_first : (subgoals -> thm -> subgoals)%}\egroup
 
-\SYNOPSIS
-This function is for internal use only and is to be deleted from a future
-version of the system. It should not be used.
-
-\ENDDOC
-\DOC{aconv}
+\DOC{allowed\_constant}
 
-\TYPE {\small\verb%aconv : (term -> term -> bool)%}\egroup
+\TYPE {\small\verb%allowed_constant : (string -> bool)%}\egroup
 
 \SYNOPSIS
-Tests for alpha-convertibility of terms.
+Tests if a string has a permissible name for a constant.
 
 \DESCRIBE
-When applied to two terms, {\small\verb%aconv%} returns {\small\verb%true%} if they are
-alpha-convertible, and {\small\verb%false%} otherwise.
+When applied to a string, {\small\verb%allowed_constant%} returns {\small\verb%true%} if the string is a
+permissible constant name, that is, if it is an identifier (see the DESCRIPTION
+for more details), and {\small\verb%false%} otherwise.
 
 \FAILURE
 Never fails.
 
 \EXAMPLE
-A simple case of alpha-convertibility is the renaming of a single quantified
-variable:
+The following shows how the lexical rules can be altered:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #aconv "?x. x=T" "?y. y=T";;
-   true : bool
+   #map allowed_constant [`pi`; `@`; `a name`; `+++++`; `*`];;
+   [true; true; false; false; true] : bool list
+
+   #new_special_symbol `+++++`;;
+   () : void
+
+   #map allowed_constant [`pi`; `@`; `a name`; `+++++`; `*`];;
+   [true; true; false; true; true] : bool list
 \end{verbatim}
 }
+\COMMENTS
+Note that this function only performs a lexical test; it does not check whether
+there is already a constant of that name in the current theory.
+
 \SEEALSO
-ALPHA, ALPHA_CONV.
+constants, is_constant, new_alphanum, new_special_symbol, special_symbols.
 
 \ENDDOC
-\DOC{activate\_binders}
+\DOC{ALL\_TAC}
 
-\TYPE {\small\verb%activate_binders : (string -> string list)%}\egroup
+\TYPE {\small\verb%ALL_TAC : tactic%}\egroup
 
 \SYNOPSIS
-Makes the quotation parser treat all binders in the current theory segment as
-such.
+Passes on a goal unchanged.
 
 \DESCRIBE
-The call
-{\par\samepage\setseps\small
-\begin{verbatim}
-   activate_binders `thy`
-\end{verbatim}
-}
-\noindent where {\small\verb%thy%} is an ancestor theory ({\small\verb%`-`%} stands for the current
-theory), will return a list of all binders on that theory, and make the parser
-treat them all as binders, that is, for each binder {\small\verb%b%}, will allow the
-syntactic sugaring {\small\verb%"b x. y"%} as a shorthand for {\small\verb%"b (\x. y)"%}. The special
-syntactic status may be suppressed by preceding {\small\verb%b%} with a dollar sign. The
-function returns a list of all the binders dealt with.
+{\small\verb%ALL_TAC%} applied to a goal {\small\verb%g%} simply produces the subgoal list {\small\verb%[g]%}. It is
+the identity for the {\small\verb%THEN%} tactical.
 
 \FAILURE
 Never fails.
 
-\COMMENTS
-This function is mainly intended for internal use. All binders declared by
-{\small\verb%new_binder%} or {\small\verb%new_binder_definition%} are always parsed as such anyway.
+\EXAMPLE
+The tactic {\small\verb%INDUCT_TAC THENL [ALL_TAC;tac]%}, applied to a goal {\small\verb%g%}, applies
+{\small\verb%INDUCT_TAC%} to {\small\verb%g%} to give a basis and step subgoal; it then returns the
+basis unchanged, along with the subgoals produced by applying {\small\verb%tac%} to the
+step.
+
+\USES
+Used to write tacticals such as {\small\verb%REPEAT%}.
+Often used as a place-holder in building compound tactics using tacticals
+such as {\small\verb%THENL%}.
 
 \SEEALSO
-activate_all_binders, binders, new_binder, parse_as_binder.
+NO_TAC, REPEAT, THENL.
 
 \ENDDOC
-\DOC{AC\_CONV}
+\DOC{ALL\_THEN}
 
-\TYPE {\small\verb%AC_CONV : ((thm # thm) -> conv)%}\egroup
+\TYPE {\small\verb%ALL_THEN : thm_tactical%}\egroup
 
 \SYNOPSIS
-Proves equality of terms using associative and commutative laws.
+Passes a theorem unchanged to a theorem-tactic.
 
 \DESCRIBE
-Suppose {\small\verb%_%} is a function, which is assumed to be infix in the following syntax,
-and {\small\verb%ath%} and {\small\verb%cth%} are theorems expressing its associativity and
-commutativity; they must be of the following form, except that any free
-variables may have arbitrary names and may be universally quantified:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ath = |- m _ (n _ p) = (m _ n) _ p
-   cth = |- m _ n = n _ m
-\end{verbatim}
-}
-\noindent Then the conversion {\small\verb%AC_CONV(ath,cth)%} will prove equations whose
-left and right sides can be made identical using these associative and
-commutative laws.
+For any theorem-tactic {\small\verb%ttac%} and theorem {\small\verb%th%}, the application {\small\verb%ALL_THEN ttac
+th%} results simply in {\small\verb%ttac th%}, that is, the theorem is passed unchanged to
+the theorem-tactic. {\small\verb%ALL_THEN%} is the identity theorem-tactical.
 
 \FAILURE
-Fails if the associative or commutative law has an invalid form, or if the
-term is not an equation between AC-equivalent terms.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #AC_CONV(ADD_ASSOC,ADD_SYM)
-   #  "x + (SUC t) + ((3 + y) + z) = 3 + (SUC t) + x + y + z";;
-   |- (x + ((SUC t) + ((3 + y) + z)) = 3 + ((SUC t) + (x + (y + z)))) = T
-\end{verbatim}
-}
+The application of {\small\verb%ALL_THEN%} to a theorem-tactic never fails. The resulting
+theorem-tactic fails under exactly the same conditions as the original one
 
-\COMMENTS
-Note that the preproved associative and commutative laws for the operators {\small\verb%+%},
-{\small\verb%*%}, {\small\verb%/\%} and {\small\verb%\/%} are already in the right form to give to {\small\verb%AC_CONV%}.
+\USES
+Writing compound tactics or tacticals, e.g. terminating list iterations
+of theorem-tacticals.
 
 \SEEALSO
-SYM_CONV.
+ALL_TAC, FAIL_TAC, NO_TAC, NO_THEN, THEN_TCL, ORELSE_TCL.
 
 \ENDDOC
-\DOC{ADD\_ASSUM}
+\DOC{ALPHA\_CONV}
 
-\TYPE {\small\verb%ADD_ASSUM : (term -> thm -> thm)%}\egroup
+\TYPE {\small\verb%ALPHA_CONV : (term -> conv)%}\egroup
 
 \SYNOPSIS
-Adds an assumption to a theorem.
+Renames the bound variable of a lambda-abstraction.
 
 \DESCRIBE
-When applied to a boolean term {\small\verb%s%} and a theorem {\small\verb%A |- t%}, the inference
-rule {\small\verb%ADD_ASSUM%} returns the theorem {\small\verb%A u {s} |- t%}.
+If {\small\verb%"x"%} is a variable of type {\small\verb%ty%} and {\small\verb%"\y.t"%} is an abstraction in which
+the bound variable {\small\verb%y%} also has type {\small\verb%ty%}, then {\small\verb%ALPHA_CONV "x" "\y.t"%}
+returns the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-       A |- t
-   --------------  ADD_ASSUM "s"
-    A u {s} |- t
+   |- (\y.t) = (\x'. t[x'/y])
 \end{verbatim}
 }
-\noindent {\small\verb%ADD_ASSUM%} performs straightforward set union with the new
-assumption; it checks for identical assumptions, but not for alpha-equivalent
-ones. The position at which the new assumption is inserted into the assumption
-list should not be relied on.
+\noindent where the variable {\small\verb%x':ty%} is a primed variant of {\small\verb%x%} chosen so
+as not to be free in {\small\verb%"\y.t"%}.
 
 \FAILURE
-Fails unless the given term has type {\small\verb%bool%}.
+{\small\verb%ALPHA_CONV "x" "tm"%} fails if {\small\verb%x%} is not a variable, if {\small\verb%tm%} is not an
+abstraction, or if {\small\verb%x%} is a variable {\small\verb%v%} and {\small\verb%tm%} is a lambda abstraction
+{\small\verb%\y.t%} but the types of {\small\verb%v%} and {\small\verb%y%} differ.
 
 \SEEALSO
-ASSUME, UNDISCH.
+ALPHA, GEN_ALPHA_CONV.
 
 \ENDDOC
-\DOC{ADD\_CONV}
+\DOC{ALPHA}
 
-\TYPE {\small\verb%ADD_CONV : conv%}\egroup
+\TYPE {\small\verb%ALPHA : (term -> term -> thm)%}\egroup
 
 \SYNOPSIS
-Computes the sum of two natural number constants.
+Proves equality of alpha-equivalent terms.
 
 \DESCRIBE
-If {\small\verb%n%} and {\small\verb%m%} are numeral constants (e.g. {\small\verb%0%}, {\small\verb%1%}, {\small\verb%2%}, {\small\verb%3%},...), then
-{\small\verb%ADD_CONV "n + m"%} returns the theorem:
+When applied to a pair of terms {\small\verb%t1%} and {\small\verb%t1'%} which are
+alpha-equivalent, {\small\verb%ALPHA%} returns the theorem {\small\verb%|- t1 = t1'%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- n + m = s
+
+   -------------  ALPHA "t1" "t1'"
+    |- t1 = t1'
 \end{verbatim}
 }
-\noindent where {\small\verb%s%} is the numeral that denotes the sum of the natural
-numbers denoted by {\small\verb%n%} and {\small\verb%m%}.
-
 \FAILURE
-{\small\verb%ADD_CONV tm%} fails if {\small\verb%tm%} is not of the form  {\small\verb%"n + m"%}, where {\small\verb%n%} and
-{\small\verb%m%} are numerals.
+Fails unless the terms provided are alpha-equivalent.
 
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#ADD_CONV "75 + 25";;
-|- 75 + 25 = 100
+#ALPHA "!x:num. x = x" "!y:num. y = y";;
+|- (!x. x = x) = (!y. y = y)
 \end{verbatim}
 }
+\COMMENTS
+The system shows the type of {\small\verb%ALPHA%} as {\small\verb%term -> conv%}.
+
+\SEEALSO
+aconv, ALPHA_CONV, GEN_ALPHA_CONV.
+
 \ENDDOC
-\DOC{allowed\_constant}
+\DOC{ancestors}
 
-\TYPE {\small\verb%allowed_constant : (string -> bool)%}\egroup
+\TYPE {\small\verb%ancestors : (string -> string list)%}\egroup
 
 \SYNOPSIS
-Tests if a string has a permissible name for a constant.
+Gets a list of the (proper) ancestors of a theory.
 
 \DESCRIBE
-When applied to a string, {\small\verb%allowed_constant%} returns {\small\verb%true%} if the string is a
-permissible constant name, that is, if it is an identifier (see the DESCRIPTION
-for more details), and {\small\verb%false%} otherwise.
+A call to {\small\verb%ancestors `th`%} returns a list of all the proper ancestors (i.e.
+parents, parents of parents, etc.) of the theory {\small\verb%th%}.
 
 \FAILURE
-Never fails.
-
-\EXAMPLE
-The following shows how the lexical rules can be altered:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #map allowed_constant [`pi`; `@`; `a name`; `+++++`; `*`];;
-   [true; true; false; false; true] : bool list
-
-   #new_special_symbol `+++++`;;
-   () : void
-
-   #map allowed_constant [`pi`; `@`; `a name`; `+++++`; `*`];;
-   [true; true; false; true; true] : bool list
-\end{verbatim}
-}
-\COMMENTS
-Note that this function only performs a lexical test; it does not check whether
-there is already a constant of that name in the current theory.
+Fails if `th` is not an ancestor of the current theory.
 
 \SEEALSO
-constants, is_constant, new_alphanum, new_special_symbol, special_symbols.
+ancestry, parents.
 
 \ENDDOC
-\DOC{ALL\_CONV}
+\DOC{ancestry}
 
-\TYPE {\small\verb%ALL_CONV : conv%}\egroup
+\TYPE {\small\verb%ancestry : (void -> string list)%}\egroup
 
 \SYNOPSIS
-Conversion that always succeeds and leaves a term unchanged.
+Gets a list of the ancestors of the current theory.
 
 \DESCRIBE
-When applied to a term {\small\verb%"t"%}, the conversion {\small\verb%ALL_CONV%} returns the
-theorem {\small\verb%|- t = t%}.
+A call {\small\verb%ancestry()%} returns a list of all the ancestors of the current theory,
+i.e. the current theory itself, its parents, parents of parents, etc.
 
 \FAILURE
 Never fails.
 
-\USES
-Identity element for {\small\verb%THENC%}.
+\COMMENTS
+The call {\small\verb%ancestry()%} is considerably more efficient than {\small\verb%ancestors `-`%}.
 
 \SEEALSO
-NO_CONV, REFL.
+ancestors, parents.
 
 \ENDDOC
-\DOC{ALL\_EL\_CONV}
+\DOC{AND\_EXISTS\_CONV}
 
-\TYPE {\small\verb%ALL_EL_CONV : conv -> conv%}\egroup
+\TYPE {\small\verb%AND_EXISTS_CONV : conv%}\egroup
 
 \SYNOPSIS
-Computes by inference the result of applying a predicate to elements of a list.
+Moves an existential quantification outwards through a conjunction.
 
 \DESCRIBE
-{\small\verb%ALL_EL_CONV%} takes a conversion {\small\verb%conv%} and a term {\small\verb%tm%} in the following form:
+When applied to a term of the form {\small\verb%(?x.P) /\ (?x.Q)%}, where {\small\verb%x%} is free
+in neither {\small\verb%P%} nor {\small\verb%Q%}, {\small\verb%AND_EXISTS_CONV%} returns the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   ALL_EL P [x0;...xn]
+   |- (?x. P) /\ (?x. Q) = (?x. P /\ Q)
 \end{verbatim}
 }
-\noindent It returns the theorem
+\FAILURE
+{\small\verb%AND_EXISTS_CONV%} fails if it is applied to a term not of the form
+{\small\verb%(?x.P) /\ (?x.Q)%}, or if it is applied to a term {\small\verb%(?x.P) /\ (?x.Q)%}
+in which the variable {\small\verb%x%} is free in either {\small\verb%P%} or {\small\verb%Q%}.
+
+\SEEALSO
+EXISTS_AND_CONV, LEFT_AND_EXISTS_CONV, RIGHT_AND_EXISTS_CONV.
+
+\ENDDOC
+\DOC{AND\_FORALL\_CONV}
+
+\TYPE {\small\verb%AND_FORALL_CONV : conv%}\egroup
+
+\SYNOPSIS
+Moves a universal quantification outwards through a conjunction.
+
+\DESCRIBE
+When applied to a term of the form {\small\verb%(!x.P) /\ (!x.Q)%}, the conversion
+{\small\verb%AND_FORALL_CONV%} returns the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- ALL_EL P [x0;...xn] = T
+   |- (!x.P) /\ (!x.Q) = (!x. P /\ Q)
 \end{verbatim}
 }
-\noindent if for every {\small\verb%xi%} occurred in the list, {\small\verb%conv "P xi"%} returns a theorem {\small\verb%|- P xi = T%}, otherwise, if for at least one {\small\verb%xi%}, evaluating 
-{\small\verb%conv "P xi"%} returns the theorem {\small\verb%|- P xi = F%}, then it returns the theorem
+\FAILURE
+Fails if applied to a term not of the form {\small\verb%(!x.P) /\ (!x.Q)%}.
+
+\SEEALSO
+FORALL_AND_CONV, LEFT_AND_FORALL_CONV, RIGHT_AND_FORALL_CONV.
+
+\ENDDOC
+\DOC{ANTE\_CONJ\_CONV}
+
+\TYPE {\small\verb%ANTE_CONJ_CONV : conv%}\egroup
+
+\SYNOPSIS
+Eliminates a conjunctive antecedent in favour of implication.
+
+\DESCRIBE
+When applied to a term of the form {\small\verb%"(t1 /\ t2) ==> t"%}, the conversion
+{\small\verb%ANTE_CONJ_CONV%} returns the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- ALL_EL P [x0;...xn] = F
+   |- (t1 /\ t2 ==> t) = (t1 ==> t2 ==> t)
 \end{verbatim}
 }
-
 \FAILURE
-{\small\verb%ALL_EL_CONV conv tm%} fails if {\small\verb%tm%} is not of the form described above, or
-failure occurs when evaluating {\small\verb%conv "P xi"%} for some {\small\verb%xi%}.
+Fails if applied to a term not of the form {\small\verb%"(t1 /\ t2) ==> t"%}.
 
-\EXAMPLE
-Evaluating
+\USES
+Somewhat ad-hoc, but can be used (with {\small\verb%CONV_TAC%}) to transform a goal of the
+form {\small\verb%?- (P /\ Q) ==> R%} into the subgoal {\small\verb%?- P ==> (Q ==> R)%}, so that only
+the antecedent {\small\verb%P%} is moved into the assumptions by {\small\verb%DISCH_TAC%}.
+
+\ENDDOC
+\DOC{ANTE\_RES\_THEN}
+
+\TYPE {\small\verb%ANTE_RES_THEN : thm_tactical%}\egroup
+
+\SYNOPSIS
+Resolves implicative assumptions with an antecedent.
+
+\DESCRIBE
+Given a theorem-tactic {\small\verb%ttac%} and a theorem {\small\verb%A |- t%}, the function
+{\small\verb%ANTE_RES_THEN%} produces a tactic that attempts to match {\small\verb%t%} to the antecedent
+of each implication
 {\par\samepage\setseps\small
 \begin{verbatim}
-   ALL_EL_CONV bool_EQ_CONV "ALL_EL ($= T) [T;F;T]";;
+   Ai |- !x1...xn. ui ==> vi
 \end{verbatim}
 }
-\noindent returns the following theorem:
+\noindent (where {\small\verb%Ai%} is just {\small\verb%!x1...xn. ui ==> vi%}) that occurs among the
+assumptions of a goal. If the antecedent {\small\verb%ui%} of any implication matches {\small\verb%t%},
+then an instance of {\small\verb%Ai u A |- vi%} is obtained by specialization of the
+variables {\small\verb%x1%}, ..., {\small\verb%xn%} and type instantiation, followed by an application of
+modus ponens.  Because all implicative assumptions are tried, this may result
+in several modus-ponens consequences of the supplied theorem and the
+assumptions.  Tactics are produced using {\small\verb%ttac%} from all these theorems, and
+these tactics are applied in sequence to the goal.  That is,
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- ALL_EL($= T)[T;F;T] = F
+   ANTE_RES_THEN ttac (A |- t) g
 \end{verbatim}
 }
-\noindent   In general, if the predicate {\small\verb%P%} is an explicit lambda abstraction
-{\small\verb%(\x. P x)%}, the conversion should be in the form
+\noindent has the effect of:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   (BETA_CONV THENC conv')
+   MAP_EVERY ttac [A1 u A |- v1; ...; Am u A |- vm] g
 \end{verbatim}
 }
-
-\SEEALSO
-SOME_EL_CONV, IS_EL_CONV, FOLDL_CONV, FOLDR_CONV, list_FOLD_CONV.
-
-\ENDDOC
-
-\DOC{ALL\_TAC}
-
-\TYPE {\small\verb%ALL_TAC : tactic%}\egroup
-
-\SYNOPSIS
-Passes on a goal unchanged.
-
-\DESCRIBE
-{\small\verb%ALL_TAC%} applied to a goal {\small\verb%g%} simply produces the subgoal list {\small\verb%[g]%}. It is
-the identity for the {\small\verb%THEN%} tactical.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-The tactic {\small\verb%INDUCT_TAC THENL [ALL_TAC;tac]%}, applied to a goal {\small\verb%g%}, applies
-{\small\verb%INDUCT_TAC%} to {\small\verb%g%} to give a basis and step subgoal; it then returns the
-basis unchanged, along with the subgoals produced by applying {\small\verb%tac%} to the
-step.
-
-\USES
-Used to write tacticals such as {\small\verb%REPEAT%}.
-Often used as a place-holder in building compound tactics using tacticals
-such as {\small\verb%THENL%}.
-
-\SEEALSO
-NO_TAC, REPEAT, THENL.
-
-\ENDDOC
-\DOC{ALL\_THEN}
-
-\TYPE {\small\verb%ALL_THEN : thm_tactical%}\egroup
-
-\SYNOPSIS
-Passes a theorem unchanged to a theorem-tactic.
-
-\DESCRIBE
-For any theorem-tactic {\small\verb%ttac%} and theorem {\small\verb%th%}, the application {\small\verb%ALL_THEN ttac
-th%} results simply in {\small\verb%ttac th%}, that is, the theorem is passed unchanged to
-the theorem-tactic. {\small\verb%ALL_THEN%} is the identity theorem-tactical.
+\noindent where the theorems {\small\verb%Ai u A |- vi%} are all the consequences that can
+be drawn by a (single) matching modus-ponens inference from the implications
+that occur among the assumptions of the goal {\small\verb%g%} and the supplied theorem
+{\small\verb%A |- t%}.  Any negation {\small\verb%~v%} that appears among the assumptions of the goal is
+treated as an implication {\small\verb%v ==> F%}.  The sequence in which the theorems
+{\small\verb%Ai u A |- vi%} are generated and the corresponding tactics applied is
+unspecified.
 
 \FAILURE
-The application of {\small\verb%ALL_THEN%} to a theorem-tactic never fails. The resulting
-theorem-tactic fails under exactly the same conditions as the original one
-
-\USES
-Writing compound tactics or tacticals, e.g. terminating list iterations
-of theorem-tacticals.
+{\small\verb%ANTE_RES_THEN ttac (A |- t)%} fails when applied to a goal {\small\verb%g%} if any of the
+tactics produced by {\small\verb%ttac (Ai u A |- vi)%}, where {\small\verb%Ai u A |- vi%} is the {\small\verb%i%}th
+resolvent obtained from the theorem {\small\verb%A |- t%} and the assumptions of {\small\verb%g%}, fails
+when applied in sequence to {\small\verb%g%}.
 
 \SEEALSO
-ALL_TAC, FAIL_TAC, NO_TAC, NO_THEN, THEN_TCL, ORELSE_TCL.
+IMP_RES_TAC, IMP_RES_THEN, MATCH_MP, RES_TAC, RES_THEN.
 
 \ENDDOC
-\DOC{ALPHA}
+\DOC{APPEND\_CONV}
 
-\TYPE {\small\verb%ALPHA : (term -> term -> thm)%}\egroup
+\TYPE {\small\verb%APPEND_CONV : conv%}\egroup
 
 \SYNOPSIS
-Proves equality of alpha-equivalent terms.
+Computes by inference the result of appending two object-language lists.
 
 \DESCRIBE
-When applied to a pair of terms {\small\verb%t1%} and {\small\verb%t1'%} which are
-alpha-equivalent, {\small\verb%ALPHA%} returns the theorem {\small\verb%|- t1 = t1'%}.
+For any pair of object language lists of the form {\small\verb%"[x1;...;xn]"%} and
+{\small\verb%"[y1;...;ym]"%}, the result of evaluating
 {\par\samepage\setseps\small
 \begin{verbatim}
-
-   -------------  ALPHA "t1" "t1'"
-    |- t1 = t1'
+   APPEND_CONV "APPEND [x1;...;xn] [y1;...;ym]"
 \end{verbatim}
 }
-\FAILURE
-Fails unless the terms provided are alpha-equivalent.
-
-\EXAMPLE
+\noindent is the theorem
 {\par\samepage\setseps\small
 \begin{verbatim}
-#ALPHA "!x:num. x = x" "!y:num. y = y";;
-|- (!x. x = x) = (!y. y = y)
+   |- APPEND [x1;...;xn] [y1;...;ym] = [x1;...;xn;y1;...;ym]
 \end{verbatim}
 }
-\COMMENTS
-The system shows the type of {\small\verb%ALPHA%} as {\small\verb%term -> conv%}.
+\noindent The length of either list (or both) may be 0.
 
-\SEEALSO
-aconv, ALPHA_CONV, GEN_ALPHA_CONV.
+\FAILURE
+{\small\verb%APPEND_CONV tm%} fails if {\small\verb%tm%} is not of the form {\small\verb%"APPEND l1 l2"%}, where
+{\small\verb%l1%} and {\small\verb%l2%} are (possibly empty) object-language lists of the forms
+{\small\verb%"[x1;...;xn]"%} and {\small\verb%"[y1;...;ym]"%}.
 
 \ENDDOC
-\DOC{ALPHA\_CONV}
 
-\TYPE {\small\verb%ALPHA_CONV : (term -> conv)%}\egroup
+\DOC{append}
+
+\TYPE {\small\verb%append : (* list -> * list -> * list)%}\egroup
 
 \SYNOPSIS
-Renames the bound variable of a lambda-abstraction.
+Concatenates two lists.
 
 \DESCRIBE
-If {\small\verb%"x"%} is a variable of type {\small\verb%ty%} and {\small\verb%"\y.t"%} is an abstraction in which
-the bound variable {\small\verb%y%} also has type {\small\verb%ty%}, then {\small\verb%ALPHA_CONV "x" "\y.t"%}
-returns the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (\y.t) = (\x'. t[x'/y])
-\end{verbatim}
-}
-\noindent where the variable {\small\verb%x':ty%} is a primed variant of {\small\verb%x%} chosen so
-as not to be free in {\small\verb%"\y.t"%}.
+{\small\verb%append [x1;...;xn] [y1;...;ym]%} returns {\small\verb%[x1;...;xn;y1;...;ym]%}.
 
 \FAILURE
-{\small\verb%ALPHA_CONV "x" "tm"%} fails if {\small\verb%x%} is not a variable, if {\small\verb%tm%} is not an
-abstraction, or if {\small\verb%x%} is a variable {\small\verb%v%} and {\small\verb%tm%} is a lambda abstraction
-{\small\verb%\y.t%} but the types of {\small\verb%v%} and {\small\verb%y%} differ.
+Never fails.
 
-\SEEALSO
-ALPHA, GEN_ALPHA_CONV.
+\COMMENTS
+Performs the same operation as {\small\verb%$@%}.
 
 \ENDDOC
-\DOC{ancestors}
+\DOC{append\_openw}
 
-\TYPE {\small\verb%ancestors : (string -> string list)%}\egroup
+\TYPE {\small\verb%append_openw : (string -> string)%}\egroup
 
 \SYNOPSIS
-Gets a list of the (proper) ancestors of a theory.
+Opens a port for appending to a named file.
 
 \DESCRIBE
-A call to {\small\verb%ancestors `th`%} returns a list of all the proper ancestors (i.e.
-parents, parents of parents, etc.) of the theory {\small\verb%th%}.
-
-\FAILURE
-Fails if `th` is not an ancestor of the current theory.
+When applied to a filename {\small\verb%`name`%}, the function {\small\verb%append_openw%} opens the file
+{\small\verb%name%} for writing, such that existing contents are appended to rather than
+overwritten. It returns a port descriptor string, which can be used by {\small\verb%write%}
+to append to the file, and by {\small\verb%close%} to close it.
 
-\SEEALSO
-ancestry, parents.
+\EXAMPLE
+The following example assumes that HOL is being run under Unix. It will
+overwrite an existing file {\small\verb%test-file%} in the current directory.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #system `echo -n 'Hello ' >test-file`;;
+   0 : int
 
-\ENDDOC
-\DOC{ancestry}
+   #let port = append_openw `test-file`;;
+   port = `%test-file` : string
 
-\TYPE {\small\verb%ancestry : (void -> string list)%}\egroup
+   #write(port,`world`);;
+   () : void
 
-\SYNOPSIS
-Gets a list of the ancestors of the current theory.
+   #close port;;
+   () : void
 
-\DESCRIBE
-A call {\small\verb%ancestry()%} returns a list of all the ancestors of the current theory,
-i.e. the current theory itself, its parents, parents of parents, etc.
+   #system `cat test-file`;;
+   Hello world0 : int
+\end{verbatim}
+}
+\SEEALSO
+close, openi, openw, read, write.
 
-\FAILURE
-Never fails.
+\ENDDOC
+\DOC{apply\_proof}
 
-\COMMENTS
-The call {\small\verb%ancestry()%} is considerably more efficient than {\small\verb%ancestors `-`%}.
+\TYPE {\small\verb%apply_proof : (subgoals -> thm)%}\egroup
 
-\SEEALSO
-ancestors, parents.
+\SYNOPSIS
+This function is for internal use only and is to be deleted from a future
+version of the system. It should not be used.
 
 \ENDDOC
-\DOC{AND\_EXISTS\_CONV}
+\DOC{AP\_TERM}
 
-\TYPE {\small\verb%AND_EXISTS_CONV : conv%}\egroup
+\TYPE {\small\verb%AP_TERM : (term -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Moves an existential quantification outwards through a conjunction.
+Applies a function to both sides of an equational theorem.
 
 \DESCRIBE
-When applied to a term of the form {\small\verb%(?x.P) /\ (?x.Q)%}, where {\small\verb%x%} is free
-in neither {\small\verb%P%} nor {\small\verb%Q%}, {\small\verb%AND_EXISTS_CONV%} returns the theorem:
+When applied to a term {\small\verb%f%} and a theorem {\small\verb%A |- x = y%}, the
+inference rule {\small\verb%AP_TERM%} returns the theorem {\small\verb%A |- f x = f y%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (?x. P) /\ (?x. Q) = (?x. P /\ Q)
+      A |- x = y
+   ----------------  AP_TERM "f"
+    A |- f x = f y
 \end{verbatim}
 }
 \FAILURE
-{\small\verb%AND_EXISTS_CONV%} fails if it is applied to a term not of the form
-{\small\verb%(?x.P) /\ (?x.Q)%}, or if it is applied to a term {\small\verb%(?x.P) /\ (?x.Q)%}
-in which the variable {\small\verb%x%} is free in either {\small\verb%P%} or {\small\verb%Q%}.
+Fails unless the theorem is equational and the supplied term is a function
+whose domain type is the same as the type of both sides of the equation.
 
 \SEEALSO
-EXISTS_AND_CONV, LEFT_AND_EXISTS_CONV, RIGHT_AND_EXISTS_CONV.
+AP_THM, MK_COMB.
 
 \ENDDOC
-\DOC{AND\_FORALL\_CONV}
+\DOC{AP\_TERM\_TAC}
 
-\TYPE {\small\verb%AND_FORALL_CONV : conv%}\egroup
+\TYPE {\small\verb%AP_TERM_TAC : tactic%}\egroup
 
 \SYNOPSIS
-Moves a universal quantification outwards through a conjunction.
+Strips a function application from both sides of an equational goal.
 
 \DESCRIBE
-When applied to a term of the form {\small\verb%(!x.P) /\ (!x.Q)%}, the conversion
-{\small\verb%AND_FORALL_CONV%} returns the theorem:
+{\small\verb%AP_TERM_TAC%} reduces a goal of the form {\small\verb%A ?- f x = f y%} by stripping away
+the function applications, giving the new goal {\small\verb%A ?- x = y%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (!x.P) /\ (!x.Q) = (!x. P /\ Q)
+    A ?- f x = f y
+   ================  AP_TERM_TAC
+     A ?- x = y
 \end{verbatim}
 }
 \FAILURE
-Fails if applied to a term not of the form {\small\verb%(!x.P) /\ (!x.Q)%}.
+Fails unless the goal is equational, with both sides being applications
+of the same function.
 
 \SEEALSO
-FORALL_AND_CONV, LEFT_AND_FORALL_CONV, RIGHT_AND_FORALL_CONV.
+AP_TERM, AP_THM.
 
 \ENDDOC
-\DOC{ANTE\_CONJ\_CONV}
+\DOC{AP\_THM}
 
-\TYPE {\small\verb%ANTE_CONJ_CONV : conv%}\egroup
+\TYPE {\small\verb%AP_THM : (thm -> term -> thm)%}\egroup
 
 \SYNOPSIS
-Eliminates a conjunctive antecedent in favour of implication.
+Proves equality of equal functions applied to a term.
 
 \DESCRIBE
-When applied to a term of the form {\small\verb%"(t1 /\ t2) ==> t"%}, the conversion
-{\small\verb%ANTE_CONJ_CONV%} returns the theorem:
+When applied to a theorem {\small\verb%A |- f = g%} and a term {\small\verb%x%}, the inference
+rule {\small\verb%AP_THM%} returns the theorem {\small\verb%A |- f x = g x%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (t1 /\ t2 ==> t) = (t1 ==> t2 ==> t)
+      A |- f = g
+   ----------------  AP_THM (A |- f = g) "x"
+    A |- f x = g x
 \end{verbatim}
 }
 \FAILURE
-Fails if applied to a term not of the form {\small\verb%"(t1 /\ t2) ==> t"%}.
+Fails unless the conclusion of the theorem is an equation, both sides
+of which are functions whose domain type is the same as that of the
+supplied term.
 
-\USES
-Somewhat ad-hoc, but can be used (with {\small\verb%CONV_TAC%}) to transform a goal of the
-form {\small\verb%?- (P /\ Q) ==> R%} into the subgoal {\small\verb%?- P ==> (Q ==> R)%}, so that only
-the antecedent {\small\verb%P%} is moved into the assumptions by {\small\verb%DISCH_TAC%}.
+\COMMENTS
+The type of {\small\verb%AP_THM%} is shown by the system as {\small\verb%thm -> conv%}.
+
+\SEEALSO
+AP_TERM, ETA_CONV, EXT, MK_COMB.
 
 \ENDDOC
-\DOC{ANTE\_RES\_THEN}
+\DOC{AP\_THM\_TAC}
 
-\TYPE {\small\verb%ANTE_RES_THEN : thm_tactical%}\egroup
+\TYPE {\small\verb%AP_THM_TAC : tactic%}\egroup
 
 \SYNOPSIS
-Resolves implicative assumptions with an antecedent.
+Strips identical operands from functions on both sides of an equation.
 
 \DESCRIBE
-Given a theorem-tactic {\small\verb%ttac%} and a theorem {\small\verb%A |- t%}, the function
-{\small\verb%ANTE_RES_THEN%} produces a tactic that attempts to match {\small\verb%t%} to the antecedent
-of each implication
+When applied to a goal of the form {\small\verb%A ?- f x = g x%}, the tactic {\small\verb%AP_THM_TAC%}
+strips away the operands of the function application:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   Ai |- !x1...xn. ui ==> vi
-\end{verbatim}
-}
-\noindent (where {\small\verb%Ai%} is just {\small\verb%!x1...xn. ui ==> vi%}) that occurs among the
-assumptions of a goal. If the antecedent {\small\verb%ui%} of any implication matches {\small\verb%t%},
-then an instance of {\small\verb%Ai u A |- vi%} is obtained by specialization of the
-variables {\small\verb%x1%}, ..., {\small\verb%xn%} and type instantiation, followed by an application of
-modus ponens.  Because all implicative assumptions are tried, this may result
-in several modus-ponens consequences of the supplied theorem and the
-assumptions.  Tactics are produced using {\small\verb%ttac%} from all these theorems, and
-these tactics are applied in sequence to the goal.  That is,
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ANTE_RES_THEN ttac (A |- t) g
-\end{verbatim}
-}
-\noindent has the effect of:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   MAP_EVERY ttac [A1 u A |- v1; ...; Am u A |- vm] g
-\end{verbatim}
-}
-\noindent where the theorems {\small\verb%Ai u A |- vi%} are all the consequences that can
-be drawn by a (single) matching modus-ponens inference from the implications
-that occur among the assumptions of the goal {\small\verb%g%} and the supplied theorem
-{\small\verb%A |- t%}.  Any negation {\small\verb%~v%} that appears among the assumptions of the goal is
-treated as an implication {\small\verb%v ==> F%}.  The sequence in which the theorems
-{\small\verb%Ai u A |- vi%} are generated and the corresponding tactics applied is
-unspecified.
-
-\FAILURE
-{\small\verb%ANTE_RES_THEN ttac (A |- t)%} fails when applied to a goal {\small\verb%g%} if any of the
-tactics produced by {\small\verb%ttac (Ai u A |- vi)%}, where {\small\verb%Ai u A |- vi%} is the {\small\verb%i%}th
-resolvent obtained from the theorem {\small\verb%A |- t%} and the assumptions of {\small\verb%g%}, fails
-when applied in sequence to {\small\verb%g%}.
-
-\SEEALSO
-IMP_RES_TAC, IMP_RES_THEN, MATCH_MP, RES_TAC, RES_THEN.
-
-\ENDDOC
-\DOC{append}
-
-\TYPE {\small\verb%append : (* list -> * list -> * list)%}\egroup
-
-\SYNOPSIS
-Concatenates two lists.
-
-\DESCRIBE
-{\small\verb%append [x1;...;xn] [y1;...;ym]%} returns {\small\verb%[x1;...;xn;y1;...;ym]%}.
-
-\FAILURE
-Never fails.
-
-\COMMENTS
-Performs the same operation as {\small\verb%$@%}.
-
-\ENDDOC
-\DOC{APPEND\_CONV}
-
-\TYPE {\small\verb%APPEND_CONV : conv%}\egroup
-
-\SYNOPSIS
-Computes by inference the result of appending two object-language lists.
-
-\DESCRIBE
-For any pair of object language lists of the form {\small\verb%"[x1;...;xn]"%} and
-{\small\verb%"[y1;...;ym]"%}, the result of evaluating
-{\par\samepage\setseps\small
-\begin{verbatim}
-   APPEND_CONV "APPEND [x1;...;xn] [y1;...;ym]"
-\end{verbatim}
-}
-\noindent is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- APPEND [x1;...;xn] [y1;...;ym] = [x1;...;xn;y1;...;ym]
-\end{verbatim}
-}
-\noindent The length of either list (or both) may be 0.
-
-\FAILURE
-{\small\verb%APPEND_CONV tm%} fails if {\small\verb%tm%} is not of the form {\small\verb%"APPEND l1 l2"%}, where
-{\small\verb%l1%} and {\small\verb%l2%} are (possibly empty) object-language lists of the forms
-{\small\verb%"[x1;...;xn]"%} and {\small\verb%"[y1;...;ym]"%}.
-
-\ENDDOC
-
-\DOC{append\_openw}
-
-\TYPE {\small\verb%append_openw : (string -> string)%}\egroup
-
-\SYNOPSIS
-Opens a port for appending to a named file.
-
-\DESCRIBE
-When applied to a filename {\small\verb%`name`%}, the function {\small\verb%append_openw%} opens the file
-{\small\verb%name%} for writing, such that existing contents are appended to rather than
-overwritten. It returns a port descriptor string, which can be used by {\small\verb%write%}
-to append to the file, and by {\small\verb%close%} to close it.
-
-\EXAMPLE
-The following example assumes that HOL is being run under Unix. It will
-overwrite an existing file {\small\verb%test-file%} in the current directory.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #system `echo -n 'Hello ' >test-file`;;
-   0 : int
-
-   #let port = append_openw `test-file`;;
-   port = `%test-file` : string
-
-   #write(port,`world`);;
-   () : void
-
-   #close port;;
-   () : void
-
-   #system `cat test-file`;;
-   Hello world0 : int
-\end{verbatim}
-}
-\SEEALSO
-close, openi, openw, read, write.
-
-\ENDDOC
-\DOC{apply\_proof}
-
-\TYPE {\small\verb%apply_proof : (subgoals -> thm)%}\egroup
-
-\SYNOPSIS
-This function is for internal use only and is to be deleted from a future
-version of the system. It should not be used.
-
-\ENDDOC
-\DOC{AP\_TERM}
-
-\TYPE {\small\verb%AP_TERM : (term -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Applies a function to both sides of an equational theorem.
-
-\DESCRIBE
-When applied to a term {\small\verb%f%} and a theorem {\small\verb%A |- x = y%}, the
-inference rule {\small\verb%AP_TERM%} returns the theorem {\small\verb%A |- f x = f y%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-      A |- x = y
-   ----------------  AP_TERM "f"
-    A |- f x = f y
-\end{verbatim}
-}
-\FAILURE
-Fails unless the theorem is equational and the supplied term is a function
-whose domain type is the same as the type of both sides of the equation.
-
-\SEEALSO
-AP_THM, MK_COMB.
-
-\ENDDOC
-\DOC{AP\_TERM\_TAC}
-
-\TYPE {\small\verb%AP_TERM_TAC : tactic%}\egroup
-
-\SYNOPSIS
-Strips a function application from both sides of an equational goal.
-
-\DESCRIBE
-{\small\verb%AP_TERM_TAC%} reduces a goal of the form {\small\verb%A ?- f x = f y%} by stripping away
-the function applications, giving the new goal {\small\verb%A ?- x = y%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A ?- f x = f y
-   ================  AP_TERM_TAC
-     A ?- x = y
-\end{verbatim}
-}
-\FAILURE
-Fails unless the goal is equational, with both sides being applications
-of the same function.
-
-\SEEALSO
-AP_TERM, AP_THM.
-
-\ENDDOC
-\DOC{AP\_THM}
-
-\TYPE {\small\verb%AP_THM : (thm -> term -> thm)%}\egroup
-
-\SYNOPSIS
-Proves equality of equal functions applied to a term.
-
-\DESCRIBE
-When applied to a theorem {\small\verb%A |- f = g%} and a term {\small\verb%x%}, the inference
-rule {\small\verb%AP_THM%} returns the theorem {\small\verb%A |- f x = g x%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-      A |- f = g
-   ----------------  AP_THM (A |- f = g) "x"
-    A |- f x = g x
-\end{verbatim}
-}
-\FAILURE
-Fails unless the conclusion of the theorem is an equation, both sides
-of which are functions whose domain type is the same as that of the
-supplied term.
-
-\COMMENTS
-The type of {\small\verb%AP_THM%} is shown by the system as {\small\verb%thm -> conv%}.
-
-\SEEALSO
-AP_TERM, ETA_CONV, EXT, MK_COMB.
-
-\ENDDOC
-\DOC{AP\_THM\_TAC}
-
-\TYPE {\small\verb%AP_THM_TAC : tactic%}\egroup
-
-\SYNOPSIS
-Strips identical operands from functions on both sides of an equation.
-
-\DESCRIBE
-When applied to a goal of the form {\small\verb%A ?- f x = g x%}, the tactic {\small\verb%AP_THM_TAC%}
-strips away the operands of the function application:
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A ?- f x = g x
-   ================  AP_THM_TAC
-      A ?- f = g
+    A ?- f x = g x
+   ================  AP_THM_TAC
+      A ?- f = g
 \end{verbatim}
 }
 \FAILURE
@@ -1149,41 +917,41 @@
 is_type.
 
 \ENDDOC
-\DOC{ascii}
+\DOC{ascii\_code}
 
-\TYPE {\small\verb%ascii : (int -> string)%}\egroup
+\TYPE {\small\verb%ascii_code : (string -> int)%}\egroup
 
 \SYNOPSIS
-Maps an integer to the corresponding ASCII character.
+Maps a character to corresponding ASCII numeric code.
 
 \DESCRIBE
-When given an integer, {\small\verb%ascii%} returns a string consisting of
-the single character corresponding to that integer under the ASCII
-encoding.
+When given a string, {\small\verb%ascii_code%} returns the numeric encoding in the
+ASCII character set of the first character of that string.
 
 \FAILURE
-Fails unless the integer supplied is in the range {\small\verb%0 <= x < 128%}.
+Fails if the string is empty ({\small\verb%``%}).
 
 \SEEALSO
-ascii_code, int_of_string, is_alphanum, is_letter, string_of_int.
+ascii, int_of_string, is_alphanum, is_letter, string_of_int.
 
 \ENDDOC
-\DOC{ascii\_code}
+\DOC{ascii}
 
-\TYPE {\small\verb%ascii_code : (string -> int)%}\egroup
+\TYPE {\small\verb%ascii : (int -> string)%}\egroup
 
 \SYNOPSIS
-Maps a character to corresponding ASCII numeric code.
+Maps an integer to the corresponding ASCII character.
 
 \DESCRIBE
-When given a string, {\small\verb%ascii_code%} returns the numeric encoding in the
-ASCII character set of the first character of that string.
+When given an integer, {\small\verb%ascii%} returns a string consisting of
+the single character corresponding to that integer under the ASCII
+encoding.
 
 \FAILURE
-Fails if the string is empty ({\small\verb%``%}).
+Fails unless the integer supplied is in the range {\small\verb%0 <= x < 128%}.
 
 \SEEALSO
-ascii, int_of_string, is_alphanum, is_letter, string_of_int.
+ascii_code, int_of_string, is_alphanum, is_letter, string_of_int.
 
 \ENDDOC
 \DOC{ASM\_CASES\_TAC}
@@ -1813,41 +1581,6 @@
 axioms, definition, load_axiom, load_axioms, new_axiom, print_theory, theorem.
 
 \ENDDOC
-\DOC{axioms}
-
-\TYPE {\small\verb%axioms : (string -> (string # thm) list)%}\egroup
-
-\SYNOPSIS
-Returns the axioms of a given theory segment of the current theory.
-
-\DESCRIBE
-A call {\small\verb%axioms `thy`%} returns the axioms of the theory segment {\small\verb%thy%} together
-with their names. The theory segment {\small\verb%thy%} must be part of the current theory.
-The names are those given to the axioms by the user when they were originally
-added to the theory segment (by a call to {\small\verb%new_axiom%}). The name of the current
-theory segment can be abbreviated by {\small\verb%`-`%}.
-
-\FAILURE
-The call {\small\verb%axioms `thy`%} will fail if the theory segment {\small\verb%thy%} is not
-part of the current theory.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#axioms `bool`;;
-[(`SELECT_AX`, |- !P x. P x ==> P($@ P));
- (`ETA_AX`, |- !t. (\x. t x) = t);
- (`IMP_ANTISYM_AX`,
-  |- !t1 t2. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 = t2));
- (`BOOL_CASES_AX`, |- !t. (t = T) \/ (t = F));
- (`ARB_THM`, |- $= = $=)]
-: (string # thm) list
-\end{verbatim}
-}
-\SEEALSO
-axiom, definitions, load_axiom, load_axioms, new_axiom, print_theory, theorems.
-
-\ENDDOC
 \DOC{axiom\_lfn}
 
 \TYPE {\small\verb%axiom_lfn : (string list -> thm)%}\egroup
@@ -1922,41 +1655,39 @@
 undo_autoload.
 
 \ENDDOC
-\DOC{B}
-
-\TYPE {\small\verb%B : ((* -> **) -> (*** -> *) -> *** -> **)%}\egroup
-
-\SYNOPSIS
-Performs curried function-composition: {\small\verb%B f g x%} = {\small\verb%f (g x)%}.
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-\#, C, CB, Co, I, K, KI, o, oo, S, W.
-
-\ENDDOC
-\DOC{b}
+\DOC{axioms}
 
-\TYPE {\small\verb%b : (void -> void)%}\egroup
+\TYPE {\small\verb%axioms : (string -> (string # thm) list)%}\egroup
 
 \SYNOPSIS
-Restores the proof state undoing the effects of a previous expansion.
+Returns the axioms of a given theory segment of the current theory.
 
 \DESCRIBE
-The function {\small\verb%b%} is part of the subgoal package. It is an abbreviation for the
-function {\small\verb%backup%}. For a description of the subgoal package, see
-{\small\verb%set_goal%}.
+A call {\small\verb%axioms `thy`%} returns the axioms of the theory segment {\small\verb%thy%} together
+with their names. The theory segment {\small\verb%thy%} must be part of the current theory.
+The names are those given to the axioms by the user when they were originally
+added to the theory segment (by a call to {\small\verb%new_axiom%}). The name of the current
+theory segment can be abbreviated by {\small\verb%`-`%}.
 
 \FAILURE
-As for {\small\verb%backup%}.
-
-\USES
-Back tracking in a goal-directed proof to undo errors or try different tactics.
+The call {\small\verb%axioms `thy`%} will fail if the theory segment {\small\verb%thy%} is not
+part of the current theory.
 
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#axioms `bool`;;
+[(`SELECT_AX`, |- !P x. P x ==> P($@ P));
+ (`ETA_AX`, |- !t. (\x. t x) = t);
+ (`IMP_ANTISYM_AX`,
+  |- !t1 t2. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 = t2));
+ (`BOOL_CASES_AX`, |- !t. (t = T) \/ (t = F));
+ (`ARB_THM`, |- $= = $=)]
+: (string # thm) list
+\end{verbatim}
+}
 \SEEALSO
-backup, backup_limit, e, expand, expandf, g, get_state, p, print_state, r,
-rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
+axiom, definitions, load_axiom, load_axioms, new_axiom, print_theory, theorems.
 
 \ENDDOC
 \DOC{backup}
@@ -2183,6 +1914,43 @@
 SND.
 
 \ENDDOC
+\DOC{b}
+
+\TYPE {\small\verb%b : (void -> void)%}\egroup
+
+\SYNOPSIS
+Restores the proof state undoing the effects of a previous expansion.
+
+\DESCRIBE
+The function {\small\verb%b%} is part of the subgoal package. It is an abbreviation for the
+function {\small\verb%backup%}. For a description of the subgoal package, see
+{\small\verb%set_goal%}.
+
+\FAILURE
+As for {\small\verb%backup%}.
+
+\USES
+Back tracking in a goal-directed proof to undo errors or try different tactics.
+
+\SEEALSO
+backup, backup_limit, e, expand, expandf, g, get_state, p, print_state, r,
+rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
+
+\ENDDOC
+\DOC{B}
+
+\TYPE {\small\verb%B : ((* -> **) -> (*** -> *) -> *** -> **)%}\egroup
+
+\SYNOPSIS
+Performs curried function-composition: {\small\verb%B f g x%} = {\small\verb%f (g x)%}.
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+\#, C, CB, Co, I, K, KI, o, oo, S, W.
+
+\ENDDOC
 \DOC{BETA\_CONV}
 
 \TYPE {\small\verb%BETA_CONV : conv%}\egroup
@@ -2339,23 +2107,6 @@
 body, dest_abs.
 
 \ENDDOC
-\DOC{body}
-
-\TYPE {\small\verb%body : (term -> term)%}\egroup
-
-\SYNOPSIS
-Returns the body of an abstraction.
-
-\DESCRIBE
-{\small\verb%body "\var. t"%} returns {\small\verb%"t"%}.
-
-\FAILURE
-Fails unless the term is an abstraction.
-
-\SEEALSO
-bndvar, dest_abs.
-
-\ENDDOC
 \DOC{BODY\_CONJUNCTS}
 
 \TYPE {\small\verb%BODY_CONJUNCTS : (thm -> thm list)%}\egroup
@@ -2393,6 +2144,23 @@
 CONJ, CONJUNCT1, CONJUNCT2, CONJUNCTS, CONJ_TAC.
 
 \ENDDOC
+\DOC{body}
+
+\TYPE {\small\verb%body : (term -> term)%}\egroup
+
+\SYNOPSIS
+Returns the body of an abstraction.
+
+\DESCRIBE
+{\small\verb%body "\var. t"%} returns {\small\verb%"t"%}.
+
+\FAILURE
+Fails unless the term is an abstraction.
+
+\SEEALSO
+bndvar, dest_abs.
+
+\ENDDOC
 \DOC{BOOL\_CASES\_TAC}
 
 \TYPE {\small\verb%BOOL_CASES_TAC : (term -> tactic)%}\egroup
@@ -2523,6 +2291,34 @@
 
 \ENDDOC
 
+\DOC{BUTLAST\_CONV}
+
+\TYPE {\small\verb%BUTLAST_CONV : conv%}\egroup
+
+\SYNOPSIS
+Computes by inference the result of stripping the last element of a list.
+
+\DESCRIBE
+For any object language list of the form {\small\verb%"[x0;...x(n-1)]"%} ,
+the result of evaluating
+{\par\samepage\setseps\small
+\begin{verbatim}
+   BUTLAST_CONV "BUTLAST [x0;...;x(n-1)]"
+\end{verbatim}
+}
+\noindent is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- BUTLAST [x0;...;x(n-1)] = [x0;...; x(n-2)]
+\end{verbatim}
+}
+
+
+\FAILURE
+{\small\verb%BUTLAST_CONV tm%} fails if {\small\verb%tm%} is an empty list.
+
+\ENDDOC
+
 \DOC{butlast}
 
 \TYPE {\small\verb%butlast : (* list -> * list)%}\egroup
@@ -2569,48 +2365,6 @@
 
 \ENDDOC
 
-\DOC{BUTLAST\_CONV}
-
-\TYPE {\small\verb%BUTLAST_CONV : conv%}\egroup
-
-\SYNOPSIS
-Computes by inference the result of stripping the last element of a list.
-
-\DESCRIBE
-For any object language list of the form {\small\verb%"[x0;...x(n-1)]"%} ,
-the result of evaluating
-{\par\samepage\setseps\small
-\begin{verbatim}
-   BUTLAST_CONV "BUTLAST [x0;...;x(n-1)]"
-\end{verbatim}
-}
-\noindent is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- BUTLAST [x0;...;x(n-1)] = [x0;...; x(n-2)]
-\end{verbatim}
-}
-
-
-\FAILURE
-{\small\verb%BUTLAST_CONV tm%} fails if {\small\verb%tm%} is an empty list.
-
-\ENDDOC
-
-\DOC{C}
-
-\TYPE {\small\verb%C : ((* -> ** -> ***) -> ** -> * -> ***)%}\egroup
-
-\SYNOPSIS
-Permutes first two arguments to curried function: {\small\verb%C f x y%} = {\small\verb%f y x%}.
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-\#, B, CB, Co, I, K, KI, o, oo, S, W.
-
-\ENDDOC
 \DOC{cached\_theories}
 
 \TYPE {\small\verb%cached_theories : (void -> (string # bool) list)%}\egroup
@@ -2756,6 +2510,20 @@
 CONTR, CONTRAPOS, CONTR_TAC, NOT_ELIM.
 
 \ENDDOC
+\DOC{C}
+
+\TYPE {\small\verb%C : ((* -> ** -> ***) -> ** -> * -> ***)%}\egroup
+
+\SYNOPSIS
+Permutes first two arguments to curried function: {\small\verb%C f x y%} = {\small\verb%f y x%}.
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+\#, B, CB, Co, I, K, KI, o, oo, S, W.
+
+\ENDDOC
 \DOC{CHANGED\_CONV}
 
 \TYPE {\small\verb%CHANGED_CONV : (conv -> conv)%}\egroup
@@ -3180,44 +2948,44 @@
 \#, B, C, CB, I, K, KI, o, oo, S, W.
 
 \ENDDOC
-\DOC{com}
+\DOC{combine}
 
-\TYPE {\small\verb%$com : ((* list # ** list) -> (* # **) list)%}\egroup
+\TYPE {\small\verb%combine : ((* list # ** list) -> (* # **) list)%}\egroup
 
 \SYNOPSIS
-Converts a pair of lists into a list of pairs (infix version).
+Converts a pair of lists into a list of pairs.
 
 \DESCRIBE
-{\small\verb%[x1;...;xn] com [y1;...;yn]%} returns {\small\verb%[(x1,y1);...;(xn,yn)]%}.
+{\small\verb%combine ([x1;...;xn],[y1;...;yn])%} returns {\small\verb%[(x1,y1);...;(xn,yn)]%}.
 
 \FAILURE
 Fails if the two lists are of different lengths.
 
 \COMMENTS
-Has the same effect as {\small\verb%combine%}.
+Has the same effect as {\small\verb%com%}.
 
 \SEEALSO
-combine, split.
+com, split.
 
 \ENDDOC
-\DOC{combine}
+\DOC{com}
 
-\TYPE {\small\verb%combine : ((* list # ** list) -> (* # **) list)%}\egroup
+\TYPE {\small\verb%$com : ((* list # ** list) -> (* # **) list)%}\egroup
 
 \SYNOPSIS
-Converts a pair of lists into a list of pairs.
+Converts a pair of lists into a list of pairs (infix version).
 
 \DESCRIBE
-{\small\verb%combine ([x1;...;xn],[y1;...;yn])%} returns {\small\verb%[(x1,y1);...;(xn,yn)]%}.
+{\small\verb%[x1;...;xn] com [y1;...;yn]%} returns {\small\verb%[(x1,y1);...;(xn,yn)]%}.
 
 \FAILURE
 Fails if the two lists are of different lengths.
 
 \COMMENTS
-Has the same effect as {\small\verb%com%}.
+Has the same effect as {\small\verb%combine%}.
 
 \SEEALSO
-com, split.
+combine, split.
 
 \ENDDOC
 \DOC{compile}
@@ -3585,6 +3353,60 @@
 {\small\verb%c%} is {\small\verb%T%} or {\small\verb%F%}, or {\small\verb%u%} and {\small\verb%v%} are alpha-equivalent.
 
 \ENDDOC
+\DOC{CONJ\_DISCH}
+
+\TYPE {\small\verb%CONJ_DISCH : (term -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Discharges an assumption and conjoins it to both sides of an equation.
+
+\DESCRIBE
+Given an term {\small\verb%t%} and a theorem {\small\verb%A |- t1 = t2%}, which is an equation between
+boolean terms, {\small\verb%CONJ_DISCH%} returns {\small\verb%A - {t} |- (t /\ t1) = (t /\ t2)%}, i.e.
+conjoins {\small\verb%t%} to both sides of the equation, removing {\small\verb%t%} from the assumptions
+if it was there.
+{\par\samepage\setseps\small
+\begin{verbatim}
+            A |- t1 = t2
+   ------------------------------  CONJ_DISCH "t"
+    A - {t} |- t /\ t1 = t /\ t2
+\end{verbatim}
+}
+\FAILURE
+Fails unless the theorem is an equation, both sides of which, and the term
+provided are of type {\small\verb%bool%}.
+
+\SEEALSO
+CONJ_DISCHL.
+
+\ENDDOC
+\DOC{CONJ\_DISCHL}
+
+\TYPE {\small\verb%CONJ_DISCHL : (term list -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Conjoins multiple assumptions to both sides of an equation.
+
+\DESCRIBE
+Given a term list {\small\verb%[t1;...;tn]%} and a theorem whose conclusion is an equation
+between boolean terms, {\small\verb%CONJ_DISCHL%} conjoins all the terms
+in the list to both sides of the equation, and removes any of the terms which
+were in the assumption list.
+{\par\samepage\setseps\small
+\begin{verbatim}
+                        A |- s = t
+   --------------------------------------------------------  CONJ_DISCHL
+    A - {t1,...,tn} |- (t1/\.../\tn/\s) = (t1/\.../\tn/\t)     ["t1";...;"tn"]
+\end{verbatim}
+}
+\FAILURE
+Fails unless the theorem is an equation, both sides of which, and all the terms
+provided, are of type {\small\verb%bool%}.
+
+\SEEALSO
+CONJ_DISCH.
+
+\ENDDOC
 \DOC{CONJ}
 
 \TYPE {\small\verb%CONJ : (thm -> thm -> thm)%}\egroup
@@ -3607,6 +3429,148 @@
 BODY_CONJUNCTS, CONJUNCT1, CONJUNCT2, CONJ_PAIR, LIST_CONJ, CONJ_LIST, CONJUNCTS.
 
 \ENDDOC
+\DOC{CONJ\_LIST}
+
+\TYPE {\small\verb%CONJ_LIST : (int -> thm -> thm list)%}\egroup
+
+\SYNOPSIS
+Extracts a list of conjuncts from a theorem (non-flattening version).
+
+\DESCRIBE
+{\small\verb%CONJ_LIST%} is the proper inverse of {\small\verb%LIST_CONJ%}. Unlike {\small\verb%CONJUNCTS%} which
+recursively splits as many conjunctions as possible both to the left and to
+the right, {\small\verb%CONJ_LIST%} splits the top-level conjunction and then splits
+(recursively) only the right conjunct. The integer argument is required
+because the term {\small\verb%tn%} may itself be a conjunction. A list of {\small\verb%n%} theorems is
+returned.
+{\par\samepage\setseps\small
+\begin{verbatim}
+    A |- t1 /\ (t2 /\ ( ... /\ tn)...)
+   ------------------------------------  CONJ_LIST n (A |- t1 /\ ... /\ tn)
+    A |- t1   A |- t2   ...   A |- tn
+\end{verbatim}
+}
+\FAILURE
+Fails if the integer argument ({\small\verb%n%}) is less than one, or if the input theorem
+has less than {\small\verb%n%} conjuncts.
+
+\EXAMPLE
+Suppose the identifier {\small\verb%th%} is bound to the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   A |- (x /\ y) /\ z /\ w
+\end{verbatim}
+}
+\noindent Here are some applications of {\small\verb%CONJ_LIST%} to {\small\verb%th%}:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #CONJ_LIST 0 th;;
+   evaluation failed     CONJ_LIST
+
+   #CONJ_LIST 1 th;;
+   [A |- (x /\ y) /\ z /\ w] : thm list
+
+   #CONJ_LIST 2 th;;
+   [A |- x /\ y; A |- z /\ w] : thm list
+
+   #CONJ_LIST 3 th;;
+   [A |- x /\ y; A |- z; A |- w] : thm list
+
+   #CONJ_LIST 4 th;;
+   evaluation failed     CONJ_LIST
+\end{verbatim}
+}
+\SEEALSO
+BODY_CONJUNCTS, LIST_CONJ, CONJUNCTS, CONJ, CONJUNCT1, CONJUNCT2, CONJ_PAIR.
+
+\ENDDOC
+\DOC{CONJ\_PAIR}
+
+\TYPE {\small\verb%CONJ_PAIR : (thm -> (thm # thm))%}\egroup
+
+\SYNOPSIS
+Extracts both conjuncts of a conjunction.
+
+\DESCRIBE
+{\par\samepage\setseps\small
+\begin{verbatim}
+       A |- t1 /\ t2
+   ----------------------  CONJ_PAIR
+    A |- t1      A |- t2
+\end{verbatim}
+}
+\noindent The two resultant theorems are returned as a pair.
+
+\FAILURE
+Fails if the input theorem is not a conjunction.
+
+\SEEALSO
+BODY_CONJUNCTS, CONJUNCT1, CONJUNCT2, CONJ, LIST_CONJ, CONJ_LIST, CONJUNCTS.
+
+\ENDDOC
+\DOC{CONJ\_SET\_CONV}
+
+\TYPE {\small\verb%CONJ_SET_CONV : (term list -> term list -> thm)%}\egroup
+
+\SYNOPSIS
+Proves the equivalence of the conjunctions of two equal sets of terms.
+
+\DESCRIBE
+The arguments to {\small\verb%CONJ_SET_CONV%} are two lists of terms {\small\verb%[t1;...;tn]%} and
+{\small\verb%[u1;...;um]%}.  If these are equal when considered as sets, that is if the sets
+{\par\samepage\setseps\small
+\begin{verbatim}
+   {t1,...,tn} and {u1,...,um}
+\end{verbatim}
+}
+\noindent are equal, then {\small\verb%CONJ_SET_CONV%} returns the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- (t1 /\ ... /\ tn) = (u1 /\ ... /\ um)
+\end{verbatim}
+}
+\noindent Otherwise {\small\verb%CONJ_SET_CONV%} fails.
+
+\FAILURE
+{\small\verb%CONJ_SET_CONV [t1;...;tn] [u1;...;um]%} fails if {\small\verb%[t1,...,tn]%} and
+{\small\verb%[u1,...,um]%}, regarded as sets of terms, are not equal. Also fails
+if any {\small\verb%ti%} or {\small\verb%ui%} does not have type {\small\verb%bool%}.
+
+\USES
+Used to order conjuncts.  First sort a list of conjuncts {\small\verb%l1%} into the
+desired order to get a new list {\small\verb%l2%}, then call {\small\verb%CONJ_SET_CONV l1 l2%}.
+
+\COMMENTS
+This is not a true conversion, so perhaps it ought to be called something else.
+
+\SEEALSO
+CONJUNCTS_CONV.
+
+\ENDDOC
+\DOC{CONJ\_TAC}
+
+\TYPE {\small\verb%CONJ_TAC : tactic%}\egroup
+
+\SYNOPSIS
+Reduces a conjunctive goal to two separate subgoals.
+
+\DESCRIBE
+When applied to a goal {\small\verb%A ?- t1 /\ t2%}, the tactic {\small\verb%CONJ_TAC%} reduces it to the
+two subgoals corresponding to each conjunct separately.
+{\par\samepage\setseps\small
+\begin{verbatim}
+       A ?- t1 /\ t2
+   ======================  CONJ_TAC
+    A ?- t1      A ?- t2
+\end{verbatim}
+}
+\FAILURE
+Fails unless the conclusion of the goal is a conjunction.
+
+\SEEALSO
+STRIP_TAC.
+
+\ENDDOC
 \DOC{CONJUNCT1}
 
 \TYPE {\small\verb%CONJUNCT1 : (thm -> thm)%}\egroup
@@ -3651,42 +3615,40 @@
 BODY_CONJUNCTS, CONJUNCT1, CONJ_PAIR, CONJ, LIST_CONJ, CONJ_LIST, CONJUNCTS.
 
 \ENDDOC
-\DOC{CONJUNCTS}
+\DOC{CONJUNCTS\_CONV}
 
-\TYPE {\small\verb%CONJUNCTS : (thm -> thm list)%}\egroup
+\TYPE {\small\verb%CONJUNCTS_CONV : ((term # term) -> thm)%}\egroup
 
 \SYNOPSIS
-Recursively splits conjunctions into a list of conjuncts.
+Prove equivalence under idempotence, symmetry and associativity of conjunction.
 
 \DESCRIBE
-Flattens out all conjuncts, regardless of grouping. Returns a singleton list
-if the input theorem is not a conjunction.
-{\par\samepage\setseps\small
-\begin{verbatim}
-       A |- t1 /\ t2 /\ ... /\ tn
-   -----------------------------------  CONJUNCTS
-    A |- t1   A |- t2   ...   A |- tn
-\end{verbatim}
-}
+{\small\verb%CONJUNCTS_CONV%} takes a pair of terms {\small\verb%"t1"%} and {\small\verb%"t2"%}, and proves
+{\small\verb%|- t1 = t2%} if {\small\verb%t1%} and {\small\verb%t2%} are equivalent up to idempotence, symmetry and
+associativity of conjunction.  That is, if {\small\verb%t1%} and {\small\verb%t2%} are two (different)
+arbitrarily-nested conjunctions of the same set of terms, then {\small\verb%CONJUNCTS_CONV
+(t1,t2)%} returns {\small\verb%|- t1 = t2%}. Otherwise, it fails.
+
 \FAILURE
-Never fails.
+Fails if {\small\verb%t1%} and {\small\verb%t2%} are not equivalent, as described above.
 
 \EXAMPLE
-Suppose the identifier {\small\verb%th%} is bound to the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   A |- (x /\ y) /\ z /\ w
-\end{verbatim}
-}
-\noindent Application of {\small\verb%CONJUNCTS%} to {\small\verb%th%} returns the following list of
-theorems:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   [A |- x; A |- y; A |- z; A |- w] : thm list
+#CONJUNCTS_CONV ("(P /\ Q) /\ R", "R /\ (Q /\ R) /\ P");;
+|- (P /\ Q) /\ R = R /\ (Q /\ R) /\ P
 \end{verbatim}
 }
+\USES
+Used to reorder a conjunction.  First sort the conjuncts in a term {\small\verb%t1%} into
+the desired order (e.g. lexicographic order, for normalization) to get a new
+term {\small\verb%t2%}, then call {\small\verb%CONJUNCTS_CONV(t1,t2)%}.
+
+\COMMENTS
+This is not a true conversion, so perhaps it ought to be called something else.
+
 \SEEALSO
-BODY_CONJUNCTS, CONJ_LIST, LIST_CONJ, CONJ, CONJUNCT1, CONJUNCT2, CONJ_PAIR.
+CONJ_SET_CONV.
 
 \ENDDOC
 \DOC{conjuncts}
@@ -3739,40 +3701,90 @@
 list_mk_conj, dest_conj.
 
 \ENDDOC
-\DOC{CONJUNCTS\_CONV}
+\DOC{CONJUNCTS}
 
-\TYPE {\small\verb%CONJUNCTS_CONV : ((term # term) -> thm)%}\egroup
+\TYPE {\small\verb%CONJUNCTS : (thm -> thm list)%}\egroup
 
 \SYNOPSIS
-Prove equivalence under idempotence, symmetry and associativity of conjunction.
+Recursively splits conjunctions into a list of conjuncts.
 
 \DESCRIBE
-{\small\verb%CONJUNCTS_CONV%} takes a pair of terms {\small\verb%"t1"%} and {\small\verb%"t2"%}, and proves
-{\small\verb%|- t1 = t2%} if {\small\verb%t1%} and {\small\verb%t2%} are equivalent up to idempotence, symmetry and
-associativity of conjunction.  That is, if {\small\verb%t1%} and {\small\verb%t2%} are two (different)
-arbitrarily-nested conjunctions of the same set of terms, then {\small\verb%CONJUNCTS_CONV
-(t1,t2)%} returns {\small\verb%|- t1 = t2%}. Otherwise, it fails.
-
+Flattens out all conjuncts, regardless of grouping. Returns a singleton list
+if the input theorem is not a conjunction.
+{\par\samepage\setseps\small
+\begin{verbatim}
+       A |- t1 /\ t2 /\ ... /\ tn
+   -----------------------------------  CONJUNCTS
+    A |- t1   A |- t2   ...   A |- tn
+\end{verbatim}
+}
 \FAILURE
-Fails if {\small\verb%t1%} and {\small\verb%t2%} are not equivalent, as described above.
+Never fails.
 
 \EXAMPLE
+Suppose the identifier {\small\verb%th%} is bound to the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-#CONJUNCTS_CONV ("(P /\ Q) /\ R", "R /\ (Q /\ R) /\ P");;
-|- (P /\ Q) /\ R = R /\ (Q /\ R) /\ P
+   A |- (x /\ y) /\ z /\ w
 \end{verbatim}
 }
-\USES
-Used to reorder a conjunction.  First sort the conjuncts in a term {\small\verb%t1%} into
-the desired order (e.g. lexicographic order, for normalization) to get a new
-term {\small\verb%t2%}, then call {\small\verb%CONJUNCTS_CONV(t1,t2)%}.
+\noindent Application of {\small\verb%CONJUNCTS%} to {\small\verb%th%} returns the following list of
+theorems:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   [A |- x; A |- y; A |- z; A |- w] : thm list
+\end{verbatim}
+}
+\SEEALSO
+BODY_CONJUNCTS, CONJ_LIST, LIST_CONJ, CONJ, CONJUNCT1, CONJUNCT2, CONJ_PAIR.
+
+\ENDDOC
+\DOC{CONJUNCTS\_THEN2}
+
+\TYPE {\small\verb%CONJUNCTS_THEN2 : (thm_tactic -> thm_tactic -> thm_tactic)%}\egroup
+
+\SYNOPSIS
+Applies two theorem-tactics to the corresponding conjuncts of a theorem.
+
+\DESCRIBE
+{\small\verb%CONJUNCTS_THEN2%} takes two theorem-tactics, {\small\verb%f1%} and {\small\verb%f2%}, and a theorem {\small\verb%t%}
+whose conclusion must be a conjunction. {\small\verb%CONJUNCTS_THEN2%} breaks {\small\verb%t%} into two
+new theorems, {\small\verb%t1%} and {\small\verb%t2%} which are {\small\verb%CONJUNCT1%} and {\small\verb%CONJUNCT2%} of {\small\verb%t%}
+respectively, and then returns the tactic {\small\verb%f1 t1 THEN f2 t2%}. Thus
+{\par\samepage\setseps\small
+\begin{verbatim}
+   CONJUNCTS_THEN2 f1 f2 (A |- l /\ r) =  f1 (A |- l) THEN f2 (A |- r)
+\end{verbatim}
+}
+\noindent so if
+{\par\samepage\setseps\small
+\begin{verbatim}
+   A1 ?- t1                     A2 ?- t2
+  ==========  f1 (A |- l)      ==========  f2 (A |- r)
+   A2 ?- t2                     A3 ?- t3
+\end{verbatim}
+}
+\noindent then
+{\par\samepage\setseps\small
+\begin{verbatim}
+    A1 ?- t1
+   ==========  CONJUNCTS_THEN2 f1 f2 (A |- l /\ r)
+    A3 ?- t3
+\end{verbatim}
+}
+\FAILURE
+{\small\verb%CONJUNCTS_THEN f%} will fail if applied to a theorem whose conclusion is not a
+conjunction.
 
 \COMMENTS
-This is not a true conversion, so perhaps it ought to be called something else.
+The system shows the type as {\small\verb%(thm_tactic -> thm_tactical)%}.
+
+\USES
+The construction of complex {\small\verb%tactical%}s like {\small\verb%CONJUNCTS_THEN%}.
 
 \SEEALSO
-CONJ_SET_CONV.
+CONJUNCT1, CONJUNCT2, CONJUNCTS, CONJUNCTS_TAC, CONJUNCTS_THEN2,
+STRIP_THM_THEN.
 
 \ENDDOC
 \DOC{CONJUNCTS\_THEN}
@@ -3839,390 +3851,146 @@
 STRIP_THM_THEN.
 
 \ENDDOC
-\DOC{CONJUNCTS\_THEN2}
+\DOC{constants}
 
-\TYPE {\small\verb%CONJUNCTS_THEN2 : (thm_tactic -> thm_tactic -> thm_tactic)%}\egroup
+\TYPE {\small\verb%constants : (string -> term list)%}\egroup
 
 \SYNOPSIS
-Applies two theorem-tactics to the corresponding conjuncts of a theorem.
+Returns a list of the constants defined in a named theory.
 
 \DESCRIBE
-{\small\verb%CONJUNCTS_THEN2%} takes two theorem-tactics, {\small\verb%f1%} and {\small\verb%f2%}, and a theorem {\small\verb%t%}
-whose conclusion must be a conjunction. {\small\verb%CONJUNCTS_THEN2%} breaks {\small\verb%t%} into two
-new theorems, {\small\verb%t1%} and {\small\verb%t2%} which are {\small\verb%CONJUNCT1%} and {\small\verb%CONJUNCT2%} of {\small\verb%t%}
-respectively, and then returns the tactic {\small\verb%f1 t1 THEN f2 t2%}. Thus
-{\par\samepage\setseps\small
-\begin{verbatim}
-   CONJUNCTS_THEN2 f1 f2 (A |- l /\ r) =  f1 (A |- l) THEN f2 (A |- r)
-\end{verbatim}
-}
-\noindent so if
+The call
 {\par\samepage\setseps\small
 \begin{verbatim}
-   A1 ?- t1                     A2 ?- t2
-  ==========  f1 (A |- l)      ==========  f2 (A |- r)
-   A2 ?- t2                     A3 ?- t3
+   constants `thy`
 \end{verbatim}
 }
-\noindent then
+\noindent where {\small\verb%thy%} is an ancestor theory (the special string {\small\verb%`-`%} means the
+current theory), returns a list of all the constants in that theory.
+
+\FAILURE
+Fails if the named theory does not exist, or is not an ancestor of the
+current theory.
+
+\EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-    A1 ?- t1
-   ==========  CONJUNCTS_THEN2 f1 f2 (A |- l /\ r)
-    A3 ?- t3
+#constants `combin`;;
+["I"; "S"; "K"; "$o"] : term list
 \end{verbatim}
 }
-\FAILURE
-{\small\verb%CONJUNCTS_THEN f%} will fail if applied to a theorem whose conclusion is not a
-conjunction.
-
-\COMMENTS
-The system shows the type as {\small\verb%(thm_tactic -> thm_tactical)%}.
-
-\USES
-The construction of complex {\small\verb%tactical%}s like {\small\verb%CONJUNCTS_THEN%}.
-
 \SEEALSO
-CONJUNCT1, CONJUNCT2, CONJUNCTS, CONJUNCTS_TAC, CONJUNCTS_THEN2,
-STRIP_THM_THEN.
+axioms, binders, definitions, infixes, theorems
 
 \ENDDOC
-\DOC{CONJ\_DISCH}
+\DOC{CONTRAPOS\_CONV}
 
-\TYPE {\small\verb%CONJ_DISCH : (term -> thm -> thm)%}\egroup
+\TYPE {\small\verb%CONTRAPOS_CONV : conv%}\egroup
 
 \SYNOPSIS
-Discharges an assumption and conjoins it to both sides of an equation.
+Proves the equivalence of an implication and its contrapositive.
 
 \DESCRIBE
-Given an term {\small\verb%t%} and a theorem {\small\verb%A |- t1 = t2%}, which is an equation between
-boolean terms, {\small\verb%CONJ_DISCH%} returns {\small\verb%A - {t} |- (t /\ t1) = (t /\ t2)%}, i.e.
-conjoins {\small\verb%t%} to both sides of the equation, removing {\small\verb%t%} from the assumptions
-if it was there.
+When applied to an implication {\small\verb%P ==> Q%}, the conversion {\small\verb%CONTRAPOS_CONV%}
+returns the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-            A |- t1 = t2
-   ------------------------------  CONJ_DISCH "t"
-    A - {t} |- t /\ t1 = t /\ t2
+   |- (P ==> Q) = (~Q ==> ~P)
 \end{verbatim}
 }
 \FAILURE
-Fails unless the theorem is an equation, both sides of which, and the term
-provided are of type {\small\verb%bool%}.
+Fails if applied to a term that is not an implication.
 
 \SEEALSO
-CONJ_DISCHL.
+CONTRAPOS.
 
 \ENDDOC
-\DOC{CONJ\_DISCHL}
+\DOC{CONTRAPOS}
 
-\TYPE {\small\verb%CONJ_DISCHL : (term list -> thm -> thm)%}\egroup
+\TYPE {\small\verb%CONTRAPOS : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Conjoins multiple assumptions to both sides of an equation.
+Deduces the contrapositive of an implication.
 
 \DESCRIBE
-Given a term list {\small\verb%[t1;...;tn]%} and a theorem whose conclusion is an equation
-between boolean terms, {\small\verb%CONJ_DISCHL%} conjoins all the terms
-in the list to both sides of the equation, and removes any of the terms which
-were in the assumption list.
+When applied to a theorem {\small\verb%A |- s ==> t%}, the inference rule {\small\verb%CONTRAPOS%}
+returns its contrapositive, {\small\verb%A |- ~t ==> ~s%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-                        A |- s = t
-   --------------------------------------------------------  CONJ_DISCHL
-    A - {t1,...,tn} |- (t1/\.../\tn/\s) = (t1/\.../\tn/\t)     ["t1";...;"tn"]
+     A |- s ==> t
+   ----------------  CONTRAPOS
+    A |- ~t ==> ~s
 \end{verbatim}
 }
 \FAILURE
-Fails unless the theorem is an equation, both sides of which, and all the terms
-provided, are of type {\small\verb%bool%}.
+Fails unless the theorem is an implication.
 
 \SEEALSO
-CONJ_DISCH.
+CCONTR, CONTR, CONTRAPOS_CONV, NOT_ELIM.
 
 \ENDDOC
-\DOC{CONJ\_LIST}
+\DOC{CONTR}
 
-\TYPE {\small\verb%CONJ_LIST : (int -> thm -> thm list)%}\egroup
+\TYPE {\small\verb%CONTR : (term -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Extracts a list of conjuncts from a theorem (non-flattening version).
+Implements the intuitionistic contradiction rule.
 
 \DESCRIBE
-{\small\verb%CONJ_LIST%} is the proper inverse of {\small\verb%LIST_CONJ%}. Unlike {\small\verb%CONJUNCTS%} which
-recursively splits as many conjunctions as possible both to the left and to
-the right, {\small\verb%CONJ_LIST%} splits the top-level conjunction and then splits
-(recursively) only the right conjunct. The integer argument is required
-because the term {\small\verb%tn%} may itself be a conjunction. A list of {\small\verb%n%} theorems is
-returned.
+When applied to a term {\small\verb%t%} and a theorem {\small\verb%A |- F%}, the inference rule {\small\verb%CONTR%}
+returns the theorem {\small\verb%A |- t%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-    A |- t1 /\ (t2 /\ ( ... /\ tn)...)
-   ------------------------------------  CONJ_LIST n (A |- t1 /\ ... /\ tn)
-    A |- t1   A |- t2   ...   A |- tn
+    A |- F
+   --------  CONTR "t"
+    A |- t
 \end{verbatim}
 }
 \FAILURE
-Fails if the integer argument ({\small\verb%n%}) is less than one, or if the input theorem
-has less than {\small\verb%n%} conjuncts.
-
-\EXAMPLE
-Suppose the identifier {\small\verb%th%} is bound to the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   A |- (x /\ y) /\ z /\ w
-\end{verbatim}
-}
-\noindent Here are some applications of {\small\verb%CONJ_LIST%} to {\small\verb%th%}:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #CONJ_LIST 0 th;;
-   evaluation failed     CONJ_LIST
-
-   #CONJ_LIST 1 th;;
-   [A |- (x /\ y) /\ z /\ w] : thm list
-
-   #CONJ_LIST 2 th;;
-   [A |- x /\ y; A |- z /\ w] : thm list
-
-   #CONJ_LIST 3 th;;
-   [A |- x /\ y; A |- z; A |- w] : thm list
+Fails unless the term has type {\small\verb%bool%} and the theorem has {\small\verb%F%} as its
+conclusion.
 
-   #CONJ_LIST 4 th;;
-   evaluation failed     CONJ_LIST
-\end{verbatim}
-}
 \SEEALSO
-BODY_CONJUNCTS, LIST_CONJ, CONJUNCTS, CONJ, CONJUNCT1, CONJUNCT2, CONJ_PAIR.
+CCONTR, CONTRAPOS, CONTR_TAC, NOT_ELIM.
 
 \ENDDOC
-\DOC{CONJ\_PAIR}
+\DOC{CONTR\_TAC}
 
-\TYPE {\small\verb%CONJ_PAIR : (thm -> (thm # thm))%}\egroup
+\TYPE {\small\verb%CONTR_TAC : thm_tactic%}\egroup
 
 \SYNOPSIS
-Extracts both conjuncts of a conjunction.
+Solves any goal from contradictory theorem.
 
 \DESCRIBE
+When applied to a contradictory theorem {\small\verb%A' |- F%}, and a goal {\small\verb%A ?- t%},
+the tactic {\small\verb%CONTR_TAC%} completely solves the goal. This is an invalid
+tactic unless {\small\verb%A'%} is a subset of {\small\verb%A%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-       A |- t1 /\ t2
-   ----------------------  CONJ_PAIR
-    A |- t1      A |- t2
+    A ?- t
+   ========  CONTR_TAC (A' |- F)
+
 \end{verbatim}
 }
-\noindent The two resultant theorems are returned as a pair.
-
 \FAILURE
-Fails if the input theorem is not a conjunction.
+Fails unless the theorem is contradictory, i.e. has {\small\verb%F%} as its conclusion.
 
 \SEEALSO
-BODY_CONJUNCTS, CONJUNCT1, CONJUNCT2, CONJ, LIST_CONJ, CONJ_LIST, CONJUNCTS.
+CHECK_ASSUME_TAC, CONTR, CCONTR, CONTRAPOS, NOT_ELIM.
 
 \ENDDOC
-\DOC{CONJ\_SET\_CONV}
+\DOC{CONV\_RULE}
 
-\TYPE {\small\verb%CONJ_SET_CONV : (term list -> term list -> thm)%}\egroup
+\TYPE {\small\verb%CONV_RULE : (conv -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Proves the equivalence of the conjunctions of two equal sets of terms.
+Makes an inference rule from a conversion.
 
 \DESCRIBE
-The arguments to {\small\verb%CONJ_SET_CONV%} are two lists of terms {\small\verb%[t1;...;tn]%} and
-{\small\verb%[u1;...;um]%}.  If these are equal when considered as sets, that is if the sets
-{\par\samepage\setseps\small
-\begin{verbatim}
-   {t1,...,tn} and {u1,...,um}
-\end{verbatim}
-}
-\noindent are equal, then {\small\verb%CONJ_SET_CONV%} returns the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (t1 /\ ... /\ tn) = (u1 /\ ... /\ um)
-\end{verbatim}
-}
-\noindent Otherwise {\small\verb%CONJ_SET_CONV%} fails.
-
-\FAILURE
-{\small\verb%CONJ_SET_CONV [t1;...;tn] [u1;...;um]%} fails if {\small\verb%[t1,...,tn]%} and
-{\small\verb%[u1,...,um]%}, regarded as sets of terms, are not equal. Also fails
-if any {\small\verb%ti%} or {\small\verb%ui%} does not have type {\small\verb%bool%}.
-
-\USES
-Used to order conjuncts.  First sort a list of conjuncts {\small\verb%l1%} into the
-desired order to get a new list {\small\verb%l2%}, then call {\small\verb%CONJ_SET_CONV l1 l2%}.
-
-\COMMENTS
-This is not a true conversion, so perhaps it ought to be called something else.
-
-\SEEALSO
-CONJUNCTS_CONV.
-
-\ENDDOC
-\DOC{CONJ\_TAC}
-
-\TYPE {\small\verb%CONJ_TAC : tactic%}\egroup
-
-\SYNOPSIS
-Reduces a conjunctive goal to two separate subgoals.
-
-\DESCRIBE
-When applied to a goal {\small\verb%A ?- t1 /\ t2%}, the tactic {\small\verb%CONJ_TAC%} reduces it to the
-two subgoals corresponding to each conjunct separately.
-{\par\samepage\setseps\small
-\begin{verbatim}
-       A ?- t1 /\ t2
-   ======================  CONJ_TAC
-    A ?- t1      A ?- t2
-\end{verbatim}
-}
-\FAILURE
-Fails unless the conclusion of the goal is a conjunction.
-
-\SEEALSO
-STRIP_TAC.
-
-\ENDDOC
-\DOC{constants}
-
-\TYPE {\small\verb%constants : (string -> term list)%}\egroup
-
-\SYNOPSIS
-Returns a list of the constants defined in a named theory.
-
-\DESCRIBE
-The call
-{\par\samepage\setseps\small
-\begin{verbatim}
-   constants `thy`
-\end{verbatim}
-}
-\noindent where {\small\verb%thy%} is an ancestor theory (the special string {\small\verb%`-`%} means the
-current theory), returns a list of all the constants in that theory.
-
-\FAILURE
-Fails if the named theory does not exist, or is not an ancestor of the
-current theory.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#constants `combin`;;
-["I"; "S"; "K"; "$o"] : term list
-\end{verbatim}
-}
-\SEEALSO
-axioms, binders, definitions, infixes, theorems
-
-\ENDDOC
-\DOC{CONTR}
-
-\TYPE {\small\verb%CONTR : (term -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Implements the intuitionistic contradiction rule.
-
-\DESCRIBE
-When applied to a term {\small\verb%t%} and a theorem {\small\verb%A |- F%}, the inference rule {\small\verb%CONTR%}
-returns the theorem {\small\verb%A |- t%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A |- F
-   --------  CONTR "t"
-    A |- t
-\end{verbatim}
-}
-\FAILURE
-Fails unless the term has type {\small\verb%bool%} and the theorem has {\small\verb%F%} as its
-conclusion.
-
-\SEEALSO
-CCONTR, CONTRAPOS, CONTR_TAC, NOT_ELIM.
-
-\ENDDOC
-\DOC{CONTRAPOS}
-
-\TYPE {\small\verb%CONTRAPOS : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Deduces the contrapositive of an implication.
-
-\DESCRIBE
-When applied to a theorem {\small\verb%A |- s ==> t%}, the inference rule {\small\verb%CONTRAPOS%}
-returns its contrapositive, {\small\verb%A |- ~t ==> ~s%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-     A |- s ==> t
-   ----------------  CONTRAPOS
-    A |- ~t ==> ~s
-\end{verbatim}
-}
-\FAILURE
-Fails unless the theorem is an implication.
-
-\SEEALSO
-CCONTR, CONTR, CONTRAPOS_CONV, NOT_ELIM.
-
-\ENDDOC
-\DOC{CONTRAPOS\_CONV}
-
-\TYPE {\small\verb%CONTRAPOS_CONV : conv%}\egroup
-
-\SYNOPSIS
-Proves the equivalence of an implication and its contrapositive.
-
-\DESCRIBE
-When applied to an implication {\small\verb%P ==> Q%}, the conversion {\small\verb%CONTRAPOS_CONV%}
-returns the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (P ==> Q) = (~Q ==> ~P)
-\end{verbatim}
-}
-\FAILURE
-Fails if applied to a term that is not an implication.
-
-\SEEALSO
-CONTRAPOS.
-
-\ENDDOC
-\DOC{CONTR\_TAC}
-
-\TYPE {\small\verb%CONTR_TAC : thm_tactic%}\egroup
-
-\SYNOPSIS
-Solves any goal from contradictory theorem.
-
-\DESCRIBE
-When applied to a contradictory theorem {\small\verb%A' |- F%}, and a goal {\small\verb%A ?- t%},
-the tactic {\small\verb%CONTR_TAC%} completely solves the goal. This is an invalid
-tactic unless {\small\verb%A'%} is a subset of {\small\verb%A%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A ?- t
-   ========  CONTR_TAC (A' |- F)
-
-\end{verbatim}
-}
-\FAILURE
-Fails unless the theorem is contradictory, i.e. has {\small\verb%F%} as its conclusion.
-
-\SEEALSO
-CHECK_ASSUME_TAC, CONTR, CCONTR, CONTRAPOS, NOT_ELIM.
-
-\ENDDOC
-\DOC{CONV\_RULE}
-
-\TYPE {\small\verb%CONV_RULE : (conv -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Makes an inference rule from a conversion.
-
-\DESCRIBE
-If {\small\verb%c%} is a conversion, then {\small\verb%CONV_RULE c%} is an inference rule that applies
-{\small\verb%c%} to the conclusion of a theorem.  That is, if {\small\verb%c%} maps a term {\small\verb%"t"%} to the
-theorem {\small\verb%|- t = t'%}, then the rule {\small\verb%CONV_RULE c%} infers {\small\verb%|- t'%} from the
-theorem {\small\verb%|- t%}.  More precisely, if {\small\verb%c "t"%} returns {\small\verb%A' |- t = t'%}, then:
+If {\small\verb%c%} is a conversion, then {\small\verb%CONV_RULE c%} is an inference rule that applies
+{\small\verb%c%} to the conclusion of a theorem.  That is, if {\small\verb%c%} maps a term {\small\verb%"t"%} to the
+theorem {\small\verb%|- t = t'%}, then the rule {\small\verb%CONV_RULE c%} infers {\small\verb%|- t'%} from the
+theorem {\small\verb%|- t%}.  More precisely, if {\small\verb%c "t"%} returns {\small\verb%A' |- t = t'%}, then:
 {\par\samepage\setseps\small
 \begin{verbatim}
        A |- t
@@ -4353,6 +4121,41 @@
 uncurry.
 
 \ENDDOC
+\DOC{DEF\_EXISTS\_RULE}
+
+\TYPE {\small\verb%DEF_EXISTS_RULE : (term -> thm)%}\egroup
+
+\SYNOPSIS
+Proves that a function defined by a definitional equation exists.
+
+\DESCRIBE
+This rule accepts a term of the form {\small\verb%"c = ..."%} or {\small\verb%"f x1 ... xn = ..."%}, the
+variables of which may be universally quantified, and returns an existential
+theorem. The resulting theorem is typically used for generating HOL
+specifications.
+
+\FAILURE
+{\small\verb%DEF_EXISTS_RULE%} fails if the definition is not an equation, if there
+is any variable in the right-hand side which does not occur in the
+left-hand side, if the definition is recursive, if there is a free type
+variable, or if the name being defined by the function is not allowed.
+
+\EXAMPLE
+The effect of this rule can be understood more clearly through an
+example:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #DEF_EXISTS_RULE "max a b = ((a < b) => b | a)" ;;
+   |- ?max. !a b. max a b = (a < b => b | a)
+\end{verbatim}
+}
+\COMMENTS
+In later versions of HOL this function may be made internal.
+
+\SEEALSO
+new_definition, new_gen_definition, new_specification.
+
+\ENDDOC
 \DOC{define\_finite\_set\_syntax}
 
 \TYPE {\small\verb%define_finite_set_syntax : ((string # string) -> void)%}\egroup
@@ -4712,62 +4515,26 @@
 axiom, definitions, load_definition, load_definitions, new_definition, print_theory, theorem.
 
 \ENDDOC
-\DOC{definitions}
+\DOC{definition\_lfn}
 
-\TYPE {\small\verb%definitions : (string -> (string # thm) list)%}\egroup
+\TYPE {\small\verb%definition_lfn : (string list -> thm)%}\egroup
 
 \SYNOPSIS
-Returns the constant definitions, type definitions and constant specifications
-of a given theory segment of the current theory.
+Loads a given definition from a given theory.
 
 \DESCRIBE
-A call of {\small\verb%definitions `thy`%} returns the definitions of the theory segment
-{\small\verb%thy%} together with their names. Constant definitions, type definitions and
-constant specifications are all retrieved by the function {\small\verb%definitions%}. The
-theory segment {\small\verb%thy%} must be part of the current theory. The names are those
-given to the definitions by the user when they were originally added to the
-theory segment (by a call, for example, to {\small\verb%new_definition%}). The name of the
-current theory segment can be abbreviated by {\small\verb%`-`%}.
+If {\small\verb%thy%} is an ancestor theory, and {\small\verb%def%} one of its definitions, then the
+call
+{\par\samepage\setseps\small
+\begin{verbatim}
+   definition_lfn [`thy`;`def`]
+\end{verbatim}
+}
+\noindent will return that definition.
 
 \FAILURE
-The call {\small\verb%definitions `thy`%} will fail if the theory segment {\small\verb%thy%} is not
-part of the current theory.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#definitions `combin`;;
-[(`I_DEF`, |- I = S K K);
- (`S_DEF`, |- S = (\f g x. f x(g x)));
- (`K_DEF`, |- K = (\x y. x));
- (`o_DEF`, |- !f g. f o g = (\x. f(g x)))]
-: (string # thm) list
-\end{verbatim}
-}
-\SEEALSO
-axioms, definition, load_definition, load_definitions, new_definition, print_theory, theorems.
-
-\ENDDOC
-\DOC{definition\_lfn}
-
-\TYPE {\small\verb%definition_lfn : (string list -> thm)%}\egroup
-
-\SYNOPSIS
-Loads a given definition from a given theory.
-
-\DESCRIBE
-If {\small\verb%thy%} is an ancestor theory, and {\small\verb%def%} one of its definitions, then the
-call
-{\par\samepage\setseps\small
-\begin{verbatim}
-   definition_lfn [`thy`;`def`]
-\end{verbatim}
-}
-\noindent will return that definition.
-
-\FAILURE
-Fails if {\small\verb%thy%} is not an ancestor theory, or if {\small\verb%def%} is not one of its
-definitions.
+Fails if {\small\verb%thy%} is not an ancestor theory, or if {\small\verb%def%} is not one of its
+definitions.
 
 \EXAMPLE
 {\par\samepage\setseps\small
@@ -4824,39 +4591,40 @@
 load_definition, load_definitions, undo_autoload.
 
 \ENDDOC
-\DOC{DEF\_EXISTS\_RULE}
+\DOC{definitions}
 
-\TYPE {\small\verb%DEF_EXISTS_RULE : (term -> thm)%}\egroup
+\TYPE {\small\verb%definitions : (string -> (string # thm) list)%}\egroup
 
 \SYNOPSIS
-Proves that a function defined by a definitional equation exists.
+Returns the constant definitions, type definitions and constant specifications
+of a given theory segment of the current theory.
 
 \DESCRIBE
-This rule accepts a term of the form {\small\verb%"c = ..."%} or {\small\verb%"f x1 ... xn = ..."%}, the
-variables of which may be universally quantified, and returns an existential
-theorem. The resulting theorem is typically used for generating HOL
-specifications.
+A call of {\small\verb%definitions `thy`%} returns the definitions of the theory segment
+{\small\verb%thy%} together with their names. Constant definitions, type definitions and
+constant specifications are all retrieved by the function {\small\verb%definitions%}. The
+theory segment {\small\verb%thy%} must be part of the current theory. The names are those
+given to the definitions by the user when they were originally added to the
+theory segment (by a call, for example, to {\small\verb%new_definition%}). The name of the
+current theory segment can be abbreviated by {\small\verb%`-`%}.
 
 \FAILURE
-{\small\verb%DEF_EXISTS_RULE%} fails if the definition is not an equation, if there
-is any variable in the right-hand side which does not occur in the
-left-hand side, if the definition is recursive, if there is a free type
-variable, or if the name being defined by the function is not allowed.
+The call {\small\verb%definitions `thy`%} will fail if the theory segment {\small\verb%thy%} is not
+part of the current theory.
 
 \EXAMPLE
-The effect of this rule can be understood more clearly through an
-example:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #DEF_EXISTS_RULE "max a b = ((a < b) => b | a)" ;;
-   |- ?max. !a b. max a b = (a < b => b | a)
+#definitions `combin`;;
+[(`I_DEF`, |- I = S K K);
+ (`S_DEF`, |- S = (\f g x. f x(g x)));
+ (`K_DEF`, |- K = (\x y. x));
+ (`o_DEF`, |- !f g. f o g = (\x. f(g x)))]
+: (string # thm) list
 \end{verbatim}
 }
-\COMMENTS
-In later versions of HOL this function may be made internal.
-
 \SEEALSO
-new_definition, new_gen_definition, new_specification.
+axioms, definition, load_definition, load_definitions, new_definition, print_theory, theorems.
 
 \ENDDOC
 \DOC{delete\_cache}
@@ -5582,31 +5350,34 @@
 POP_ASSUM, POP_ASSUM_LIST.
 
 \ENDDOC
-\DOC{DISCH}
+\DOC{DISCH\_ALL}
 
-\TYPE {\small\verb%DISCH : (term -> thm -> thm)%}\egroup
+\TYPE {\small\verb%DISCH_ALL : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Discharges an assumption.
+Discharges all hypotheses of a theorem.
 
 \DESCRIBE
 {\par\samepage\setseps\small
 \begin{verbatim}
-       A |- t
---------------------  DISCH "u"
- A - {u} |- u ==> t
+         A1, ..., An |- t
+   ----------------------------  DISCH_ALL
+    |- A1 ==> ... ==> An ==> t
 \end{verbatim}
 }
 \FAILURE
-{\small\verb%DISCH%} will fail if {\small\verb%"u"%} is not boolean.
+{\small\verb%DISCH_ALL%} will not fail if there are no hypotheses to discharge, it will
+simply return the theorem unchanged.
 
 \COMMENTS
-The term {\small\verb%"u"%} need not be a hypothesis.  Discharging {\small\verb%"u"%} will remove all
-identical and alpha-equivalent hypotheses.
+Users should not rely on the hypotheses being discharged in any particular
+order.  Two or more alpha-convertible hypotheses will be discharged by a
+single implication; users should not rely on which hypothesis appears in the
+implication.
 
 \SEEALSO
-DISCH_ALL, DISCH_TAC, DISCH_THEN, FILTER_DISCH_TAC, FILTER_DISCH_THEN,
-NEG_DISCH, STRIP_TAC, UNDISCH, UNDISCH_ALL, UNDISCH_TAC.
+DISCH, DISCH_TAC, DISCH_THEN, NEG_DISCH, FILTER_DISCH_TAC, FILTER_DISCH_THEN,
+STRIP_TAC, UNDISCH, UNDISCH_ALL, UNDISCH_TAC.
 
 \ENDDOC
 \DOC{disch}
@@ -5632,34 +5403,31 @@
 filter.
 
 \ENDDOC
-\DOC{DISCH\_ALL}
+\DOC{DISCH}
 
-\TYPE {\small\verb%DISCH_ALL : (thm -> thm)%}\egroup
+\TYPE {\small\verb%DISCH : (term -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Discharges all hypotheses of a theorem.
+Discharges an assumption.
 
 \DESCRIBE
 {\par\samepage\setseps\small
 \begin{verbatim}
-         A1, ..., An |- t
-   ----------------------------  DISCH_ALL
-    |- A1 ==> ... ==> An ==> t
+       A |- t
+--------------------  DISCH "u"
+ A - {u} |- u ==> t
 \end{verbatim}
 }
 \FAILURE
-{\small\verb%DISCH_ALL%} will not fail if there are no hypotheses to discharge, it will
-simply return the theorem unchanged.
+{\small\verb%DISCH%} will fail if {\small\verb%"u"%} is not boolean.
 
 \COMMENTS
-Users should not rely on the hypotheses being discharged in any particular
-order.  Two or more alpha-convertible hypotheses will be discharged by a
-single implication; users should not rely on which hypothesis appears in the
-implication.
+The term {\small\verb%"u"%} need not be a hypothesis.  Discharging {\small\verb%"u"%} will remove all
+identical and alpha-equivalent hypotheses.
 
 \SEEALSO
-DISCH, DISCH_TAC, DISCH_THEN, NEG_DISCH, FILTER_DISCH_TAC, FILTER_DISCH_THEN,
-STRIP_TAC, UNDISCH, UNDISCH_ALL, UNDISCH_TAC.
+DISCH_ALL, DISCH_TAC, DISCH_THEN, FILTER_DISCH_TAC, FILTER_DISCH_THEN,
+NEG_DISCH, STRIP_TAC, UNDISCH, UNDISCH_ALL, UNDISCH_TAC.
 
 \ENDDOC
 \DOC{DISCH\_TAC}
@@ -5861,55 +5629,6 @@
 DISJ1, DISJ1_TAC, DISJ2.
 
 \ENDDOC
-\DOC{disjuncts}
-
-\TYPE {\small\verb%disjuncts : (term -> term list)%}\egroup
-
-\SYNOPSIS
-Iteratively breaks apart a disjunction.
-
-\DESCRIBE
-{\small\verb%disjuncts "t1 \/ ... \/ tn"%} returns {\small\verb%["t1";...;"tn"]%}.
-The argument term may be any tree of disjunctions;
-it need not have the form {\small\verb%"t1 \/ (t2 \/ ( ... \/ tn)...)"%}.
-A term that is not a disjunction is simply returned as the sole element of a
-list. Note that
-{\par\samepage\setseps\small
-\begin{verbatim}
-   disjuncts(list_mk_disj(["t1";...;"tn"]))
-\end{verbatim}
-}
-\noindent will not return {\small\verb%["t1";...;"tn"]%} if any of {\small\verb%t1%},...,{\small\verb%tn%} are
-disjunctions.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#list_mk_disj ["a \/ b";"c \/ d";"e \/ f"];;
-"(a \/ b) \/ (c \/ d) \/ e \/ f" : term
-
-#disjuncts it;;
-["a"; "b"; "c"; "d"; "e"; "f"] : term list
-
-#list_mk_disj it;;
-"a \/ b \/ c \/ d \/ e \/ f" : term
-
-#disjuncts "1";;
-["1"] : term list
-\end{verbatim}
-}
-\COMMENTS
-Because {\small\verb%disjuncts%} splits both the left and right sides of a disjunction,
-this operation is not the inverse of {\small\verb%list_mk_disj%}. It may be useful to
-introduce {\small\verb%list_dest_disj%} for splitting only the right tails of a disjunction.
-
-\SEEALSO
-list_mk_disj, dest_disj.
-
-\ENDDOC
 \DOC{DISJ\_CASES}
 
 \TYPE {\small\verb%DISJ_CASES : (thm -> thm -> thm -> thm)%}\egroup
@@ -6003,77 +5722,6 @@
 ASSUME_TAC, ASM_CASES_TAC, COND_CASES_TAC, DISJ_CASES_THEN, STRUCT_CASES_TAC.
 
 \ENDDOC
-\DOC{DISJ\_CASES\_THEN}
-
-\TYPE {\small\verb%DISJ_CASES_THEN : thm_tactical%}\egroup
-
-\SYNOPSIS
-Applies a theorem-tactic to each disjunct of a disjunctive theorem.
-
-\DESCRIBE
-If the theorem-tactic {\small\verb%f:thm->tactic%} applied to either
-{\small\verb%ASSUME%}d disjunct produces results as follows when applied to a goal
-{\small\verb%(A ?- t)%}:
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A ?- t                                A ?- t
-   =========  f (u |- u)      and        =========  f (v |- v)
-    A ?- t1                               A ?- t2
-\end{verbatim}
-}
-\noindent then applying {\small\verb%DISJ_CASES_THEN f (|- u \/ v)%}
-to the goal {\small\verb%(A ?- t)%} produces two subgoals.
-{\par\samepage\setseps\small
-\begin{verbatim}
-           A ?- t
-   ======================  DISJ_CASES_THEN f (|- u \/ v)
-    A ?- t1      A ?- t2
-\end{verbatim}
-}
-\FAILURE
-Fails if the theorem is not a disjunction.  An invalid tactic is
-produced if the theorem has any hypothesis which is not
-alpha-convertible to an assumption of the goal.
-
-\EXAMPLE
-Given the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   th = |- (m = 0) \/ (?n. m = SUC n)
-\end{verbatim}
-}
-\noindent and a goal of the form {\small\verb%?- (PRE m = m) = (m = 0)%},
-applying the tactic
-{\par\samepage\setseps\small
-\begin{verbatim}
-   DISJ_CASES_THEN ASSUME_TAC th
-\end{verbatim}
-}
-\noindent produces two subgoals, each with one disjunct as an added
-assumption:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ?n. m = SUC n ?- (PRE m = m) = (m = 0)
-
-   m = 0 ?- (PRE m = m) = (m = 0)
-\end{verbatim}
-}
-\USES
-Building cases tactics. For example, {\small\verb%DISJ_CASES_TAC%} could be defined by:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   let DISJ_CASES_TAC = DISJ_CASES_THEN ASSUME_TAC
-\end{verbatim}
-}
-\COMMENTS
-Use {\small\verb%DISJ_CASES_THEN2%} to apply different tactic generating functions
-to each case.
-
-\SEEALSO
-STRIP_THM_THEN, CHOOSE_THEN, CONJUNCTS_THEN, CONJUNCTS_THEN2,
-DISJ_CASES_TAC, DISJ_CASES_THEN2, DISJ_CASES_THENL.
-
-\ENDDOC
 \DOC{DISJ\_CASES\_THEN2}
 
 \TYPE {\small\verb%DISJ_CASES_THEN2 : (thm_tactic -> thm_tactical)%}\egroup
@@ -6156,21 +5804,92 @@
 DISJ_CASES_THEN, DISJ_CASES_THENL.
 
 \ENDDOC
-\DOC{DISJ\_CASES\_THENL}
+\DOC{DISJ\_CASES\_THEN}
 
-\TYPE {\small\verb%DISJ_CASES_THENL : (thm_tactic list -> thm_tactic)%}\egroup
+\TYPE {\small\verb%DISJ_CASES_THEN : thm_tactical%}\egroup
 
 \SYNOPSIS
-Applies theorem-tactics in a list to the corresponding disjuncts in a theorem.
+Applies a theorem-tactic to each disjunct of a disjunctive theorem.
 
 \DESCRIBE
-If the theorem-tactics {\small\verb%f1...fn%} applied to the {\small\verb%ASSUME%}d disjuncts of a
-theorem
+If the theorem-tactic {\small\verb%f:thm->tactic%} applied to either
+{\small\verb%ASSUME%}d disjunct produces results as follows when applied to a goal
+{\small\verb%(A ?- t)%}:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- d1 \/ d2 \/...\/ dn
-\end{verbatim}
-}
+    A ?- t                                A ?- t
+   =========  f (u |- u)      and        =========  f (v |- v)
+    A ?- t1                               A ?- t2
+\end{verbatim}
+}
+\noindent then applying {\small\verb%DISJ_CASES_THEN f (|- u \/ v)%}
+to the goal {\small\verb%(A ?- t)%} produces two subgoals.
+{\par\samepage\setseps\small
+\begin{verbatim}
+           A ?- t
+   ======================  DISJ_CASES_THEN f (|- u \/ v)
+    A ?- t1      A ?- t2
+\end{verbatim}
+}
+\FAILURE
+Fails if the theorem is not a disjunction.  An invalid tactic is
+produced if the theorem has any hypothesis which is not
+alpha-convertible to an assumption of the goal.
+
+\EXAMPLE
+Given the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   th = |- (m = 0) \/ (?n. m = SUC n)
+\end{verbatim}
+}
+\noindent and a goal of the form {\small\verb%?- (PRE m = m) = (m = 0)%},
+applying the tactic
+{\par\samepage\setseps\small
+\begin{verbatim}
+   DISJ_CASES_THEN ASSUME_TAC th
+\end{verbatim}
+}
+\noindent produces two subgoals, each with one disjunct as an added
+assumption:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   ?n. m = SUC n ?- (PRE m = m) = (m = 0)
+
+   m = 0 ?- (PRE m = m) = (m = 0)
+\end{verbatim}
+}
+\USES
+Building cases tactics. For example, {\small\verb%DISJ_CASES_TAC%} could be defined by:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   let DISJ_CASES_TAC = DISJ_CASES_THEN ASSUME_TAC
+\end{verbatim}
+}
+\COMMENTS
+Use {\small\verb%DISJ_CASES_THEN2%} to apply different tactic generating functions
+to each case.
+
+\SEEALSO
+STRIP_THM_THEN, CHOOSE_THEN, CONJUNCTS_THEN, CONJUNCTS_THEN2,
+DISJ_CASES_TAC, DISJ_CASES_THEN2, DISJ_CASES_THENL.
+
+\ENDDOC
+\DOC{DISJ\_CASES\_THENL}
+
+\TYPE {\small\verb%DISJ_CASES_THENL : (thm_tactic list -> thm_tactic)%}\egroup
+
+\SYNOPSIS
+Applies theorem-tactics in a list to the corresponding disjuncts in a theorem.
+
+\DESCRIBE
+If the theorem-tactics {\small\verb%f1...fn%} applied to the {\small\verb%ASSUME%}d disjuncts of a
+theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- d1 \/ d2 \/...\/ dn
+\end{verbatim}
+}
 \noindent produce results as follows when applied to a goal {\small\verb%(A ?- t)%}:
 {\par\samepage\setseps\small
 \begin{verbatim}
@@ -6211,103 +5930,352 @@
 \TYPE {\small\verb%DISJ_CASES_UNION : (thm -> thm -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Makes an inference for each arm of a disjunct.
+Makes an inference for each arm of a disjunct.
+
+\DESCRIBE
+Given a disjunctive theorem, and two additional theorems each having one
+disjunct as a hypothesis, a new theorem with a conclusion that is the
+disjunction of the conclusions of the last two theorems is produced. The
+hypotheses include the union of hypotheses of all three theorems less the two
+disjuncts.
+{\par\samepage\setseps\small
+\begin{verbatim}
+    A |- t1 \/ t2    A1 u {t1} |- t3     A2 u {t2} |- t4
+   ------------------------------------------------------  DISJ_CASES_UNION
+                 A u A1 u A2 |- t3 \/ t4
+\end{verbatim}
+}
+\FAILURE
+Fails if the first theorem is not a disjunction.
+
+\EXAMPLE
+The built-in theorem {\small\verb%LESS_CASES%} can be specialized to:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   th1 = |- m < n \/ n <= m
+\end{verbatim}
+}
+\noindent and used with two additional theorems:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   th2 = (m < n |- (m MOD n = m))
+   th3 = ({0 < n, n <= m} |- (m MOD n) = ((m - n) MOD n))
+\end{verbatim}
+}
+\noindent to derive a new theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #DISJ_CASES_UNION th1 th2 th3;;
+   ["0 < n"] |- (m MOD n = m) \/ (m MOD n = (m - n) MOD n)
+\end{verbatim}
+}
+\SEEALSO
+DISJ_CASES, DISJ_CASES_TAC, DISJ1, DISJ2.
+
+\ENDDOC
+\DOC{DISJ\_IMP}
+
+\TYPE {\small\verb%DISJ_IMP : (thm -> thm)%}\egroup
+
+\SYNOPSIS
+Converts a disjunctive theorem to an equivalent implicative theorem.
+
+\DESCRIBE
+The left disjunct of a disjunctive theorem becomes the negated
+antecedent of the newly generated theorem.
+{\par\samepage\setseps\small
+\begin{verbatim}
+     A |- t1 \/ t2
+   -----------------  DISJ_IMP
+    A |- ~t1 ==> t2
+\end{verbatim}
+}
+\FAILURE
+Fails if the theorem is not a disjunction.
+
+\EXAMPLE
+Specializing the built-in theorem {\small\verb%LESS_CASES%} gives the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   th = |- m < n \/ n <= m
+\end{verbatim}
+}
+\noindent to which {\small\verb%DISJ_IMP%} may be applied:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #DISJ_IMP th;;
+   |- ~m < n ==> n <= m
+\end{verbatim}
+}
+\SEEALSO
+DISJ_CASES.
+
+\ENDDOC
+\DOC{disjuncts}
+
+\TYPE {\small\verb%disjuncts : (term -> term list)%}\egroup
+
+\SYNOPSIS
+Iteratively breaks apart a disjunction.
+
+\DESCRIBE
+{\small\verb%disjuncts "t1 \/ ... \/ tn"%} returns {\small\verb%["t1";...;"tn"]%}.
+The argument term may be any tree of disjunctions;
+it need not have the form {\small\verb%"t1 \/ (t2 \/ ( ... \/ tn)...)"%}.
+A term that is not a disjunction is simply returned as the sole element of a
+list. Note that
+{\par\samepage\setseps\small
+\begin{verbatim}
+   disjuncts(list_mk_disj(["t1";...;"tn"]))
+\end{verbatim}
+}
+\noindent will not return {\small\verb%["t1";...;"tn"]%} if any of {\small\verb%t1%},...,{\small\verb%tn%} are
+disjunctions.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#list_mk_disj ["a \/ b";"c \/ d";"e \/ f"];;
+"(a \/ b) \/ (c \/ d) \/ e \/ f" : term
+
+#disjuncts it;;
+["a"; "b"; "c"; "d"; "e"; "f"] : term list
+
+#list_mk_disj it;;
+"a \/ b \/ c \/ d \/ e \/ f" : term
+
+#disjuncts "1";;
+["1"] : term list
+\end{verbatim}
+}
+\COMMENTS
+Because {\small\verb%disjuncts%} splits both the left and right sides of a disjunction,
+this operation is not the inverse of {\small\verb%list_mk_disj%}. It may be useful to
+introduce {\small\verb%list_dest_disj%} for splitting only the right tails of a disjunction.
+
+\SEEALSO
+list_mk_disj, dest_disj.
+
+\ENDDOC
+\DOC{distinct}
+
+\TYPE {\small\verb%distinct : (* list -> bool)%}\egroup
+
+\SYNOPSIS
+Checks whether the elements of a list are all distinct.
+
+\DESCRIBE
+If all the elements in a list are distinct, returns {\small\verb%true%}, otherwise returns
+{\small\verb%false%}.
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+setify.
+
+\ENDDOC
+\DOC{/}
+
+\TYPE {\small\verb%$/ : ((int # int) -> int)%}\egroup
+
+\SYNOPSIS
+Performs division on ML integers.
+
+\FAILURE
+Fails on division by zero.
+
+\ENDDOC
+\DOC{<<}
+
+\TYPE {\small\verb%$<< : ((* # **) -> bool)%}\egroup
+
+\SYNOPSIS
+Performs a lexical comparison of values.
+
+\DESCRIBE
+{\small\verb%$<<%} performs a fast ordering on values.  It is substitutive with
+respect to equality in ML (i.e. if {\small\verb%x << y%} and {\small\verb%x = x'%} and {\small\verb%y = y'%}
+then {\small\verb%x' << y'%}).
+
+\FAILURE
+Never fails.
+
+\USES
+It is often useful, for example in normalizing terms in some way, to be able to
+impose some arbitrary (but definite) ordering on ML values.
+
+\SEEALSO
+=.
+
+\ENDDOC
+\DOC{<}
+
+\TYPE {\small\verb%$< : ((int # int) -> bool)%}\egroup
+
+\SYNOPSIS
+Performs a less-than test on ML integers.
+
+\FAILURE
+Never fails.
+
+\ENDDOC
+\DOC{=}
+
+\TYPE {\small\verb%$= : ((* # *) -> bool)%}\egroup
+
+\SYNOPSIS
+Performs an equality test on two ML values.
+
+\DESCRIBE
+{\small\verb%$=%} works as expected on non-function types.  It may give unexpected results
+when applied to function types (or types containing them, such as a pair of
+functions), and should be considered unreliable in those situations.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#1 = 2;;
+false : bool
+
+#1 = 1;;
+true : bool
+
+#let f x = x + 1 and g x = x + 2;;
+f = - : (int -> int)
+g = - : (int -> int)
+
+#let f' = f and h x = f x and h' x = x + 1;;
+f' = - : (int -> int)
+h = - : (int -> int)
+h' = - : (int -> int)
+
+#f=f;;
+true : bool
+
+#f = f';;
+true : bool
+
+#f = g;;
+false : bool
+
+#f =h;;
+false : bool
+
+#f=h';;
+false : bool
+
+#h = h';;
+false : bool
+\end{verbatim}
+}
+\ENDDOC
+\DOC{>}
+
+\TYPE {\small\verb%$> : ((int # int) -> bool)%}\egroup
+
+\SYNOPSIS
+Performs a greater-than test on ML integers.
+
+\FAILURE
+Never fails.
+
+\ENDDOC
+\DOC{-}
+
+\TYPE {\small\verb%$- : ((int # int) -> int)%}\egroup
+
+\SYNOPSIS
+Performs subtraction on ML integers.
+
+\FAILURE
+Never fails.
+
+\COMMENTS
+Unary {\small\verb%-%} exists as an internal parser object, but not as a function.  So,
+whilst typing in {\small\verb%-1;;%} will work, {\small\verb%-;;%} will return a parse error.
+
+\ENDDOC
+\DOC{\char'056}
+
+\TYPE {\small\verb%$. : ((* # * list) -> * list)%}\egroup
+
+\SYNOPSIS
+Adds single element to the head of a list.
+
+\DESCRIBE
+The {\small\verb%.%} operator is an infixed primitive list constructor, analogous to {\small\verb%CONS%}
+in LISP. Its effect is {\small\verb%x . [x1;....;xn]%} = {\small\verb%[x;x1;...;xn]%}.
+
+\FAILURE
+Never fails.
+
+\ENDDOC
+\DOC{\char'100}
+
+\TYPE {\small\verb%$@ : ((* list # * list) -> * list)%}\egroup
+
+\SYNOPSIS
+Concatenates two lists.
 
 \DESCRIBE
-Given a disjunctive theorem, and two additional theorems each having one
-disjunct as a hypothesis, a new theorem with a conclusion that is the
-disjunction of the conclusions of the last two theorems is produced. The
-hypotheses include the union of hypotheses of all three theorems less the two
-disjuncts.
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A |- t1 \/ t2    A1 u {t1} |- t3     A2 u {t2} |- t4
-   ------------------------------------------------------  DISJ_CASES_UNION
-                 A u A1 u A2 |- t3 \/ t4
-\end{verbatim}
-}
+{\small\verb%@%} is an infix operator which concatenates two lists.
+
 \FAILURE
-Fails if the first theorem is not a disjunction.
+Never fails.
 
 \EXAMPLE
-The built-in theorem {\small\verb%LESS_CASES%} can be specialized to:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   th1 = |- m < n \/ n <= m
-\end{verbatim}
-}
-\noindent and used with two additional theorems:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   th2 = (m < n |- (m MOD n = m))
-   th3 = ({0 < n, n <= m} |- (m MOD n) = ((m - n) MOD n))
-\end{verbatim}
-}
-\noindent to derive a new theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #DISJ_CASES_UNION th1 th2 th3;;
-   ["0 < n"] |- (m MOD n = m) \/ (m MOD n = (m - n) MOD n)
+#[1;2;3] @ [4;5;6];;
+[1; 2; 3; 4; 5; 6] : int list
 \end{verbatim}
 }
 \SEEALSO
-DISJ_CASES, DISJ_CASES_TAC, DISJ1, DISJ2.
+append.
 
 \ENDDOC
-\DOC{DISJ\_IMP}
+\DOC{*}
 
-\TYPE {\small\verb%DISJ_IMP : (thm -> thm)%}\egroup
+\TYPE {\small\verb%$* : ((int # int) -> int)%}\egroup
 
 \SYNOPSIS
-Converts a disjunctive theorem to an equivalent implicative theorem.
+Performs multiplication on ML integers.
 
-\DESCRIBE
-The left disjunct of a disjunctive theorem becomes the negated
-antecedent of the newly generated theorem.
-{\par\samepage\setseps\small
-\begin{verbatim}
-     A |- t1 \/ t2
-   -----------------  DISJ_IMP
-    A |- ~t1 ==> t2
-\end{verbatim}
-}
 \FAILURE
-Fails if the theorem is not a disjunction.
-
-\EXAMPLE
-Specializing the built-in theorem {\small\verb%LESS_CASES%} gives the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   th = |- m < n \/ n <= m
-\end{verbatim}
-}
-\noindent to which {\small\verb%DISJ_IMP%} may be applied:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #DISJ_IMP th;;
-   |- ~m < n ==> n <= m
-\end{verbatim}
-}
-\SEEALSO
-DISJ_CASES.
+Never fails.
 
 \ENDDOC
-\DOC{distinct}
 
-\TYPE {\small\verb%distinct : (* list -> bool)%}\egroup
+\DOC{\#}
 
-\SYNOPSIS
-Checks whether the elements of a list are all distinct.
+\TYPE {\small\verb%$# : (((* -> **) # (*** -> ****)) -> (* # ***) -> (** # ****))%}\egroup
 
-\DESCRIBE
-If all the elements in a list are distinct, returns {\small\verb%true%}, otherwise returns
-{\small\verb%false%}.
+\SYNOPSIS
+Applies two functions to a pair: {\small\verb%(f # g) (x,y)%} = {\small\verb%(f x, g y)%}.
 
 \FAILURE
 Never fails.
 
 \SEEALSO
-setify.
+B, C, CB, Co, I, K, KI, o, oo, S, W.
+
+\ENDDOC
+\DOC{+}
+
+\TYPE {\small\verb%$+ : ((int # int) -> int)%}\egroup
+
+\SYNOPSIS
+Performs addition on ML integers.
+
+\FAILURE
+Never fails.
 
 \ENDDOC
 \DOC{do}
@@ -6468,6 +6436,38 @@
 rotate, save_top_thm, set_goal, set_state, top_goal, top_thm, VALID.
 
 \ENDDOC
+\DOC{EL\_CONV}
+
+\TYPE {\small\verb%EL_CONV : conv%}\egroup
+
+\SYNOPSIS
+Computes by inference the result of indexing an element from a list.
+
+\DESCRIBE
+For any object language list of the form {\small\verb%"[x0;...xk;...;xn]"%} ,
+the result of evaluating
+{\par\samepage\setseps\small
+\begin{verbatim}
+   EL_CONV "EL k [x0;...xk;...;xn]"
+\end{verbatim}
+}
+\noindent is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- EL k [x0;...;xk;...;xn] = xk
+\end{verbatim}
+}
+
+
+\FAILURE
+{\small\verb%EL_CONV tm%} fails if {\small\verb%tm%} is not of the form described above, 
+or {\small\verb%k%} is not less than the length of the list.
+
+\SEEALSO
+ELL_CONV
+
+\ENDDOC
+
 \DOC{el}
 
 \TYPE {\small\verb%el : (int -> * list -> *)%}\egroup
@@ -6527,38 +6527,6 @@
 
 \ENDDOC
 
-\DOC{EL\_CONV}
-
-\TYPE {\small\verb%EL_CONV : conv%}\egroup
-
-\SYNOPSIS
-Computes by inference the result of indexing an element from a list.
-
-\DESCRIBE
-For any object language list of the form {\small\verb%"[x0;...xk;...;xn]"%} ,
-the result of evaluating
-{\par\samepage\setseps\small
-\begin{verbatim}
-   EL_CONV "EL k [x0;...xk;...;xn]"
-\end{verbatim}
-}
-\noindent is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- EL k [x0;...;xk;...;xn] = xk
-\end{verbatim}
-}
-
-
-\FAILURE
-{\small\verb%EL_CONV tm%} fails if {\small\verb%tm%} is not of the form described above, 
-or {\small\verb%k%} is not less than the length of the list.
-
-\SEEALSO
-ELL_CONV
-
-\ENDDOC
-
 \DOC{end\_itlist}
 
 \TYPE {\small\verb%end_itlist : ((* -> * -> *) -> * list -> *)%}\egroup
@@ -6656,51 +6624,6 @@
 EQF_ELIM, EQT_ELIM, EQT_INTRO.
 
 \ENDDOC
-\DOC{EQT\_ELIM}
-
-\TYPE {\small\verb%EQT_ELIM : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Eliminates equality with {\small\verb%T%}.
-
-\DESCRIBE
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A |- tm = T
-   -------------  EQT_ELIM
-      A |- tm
-\end{verbatim}
-}
-\FAILURE
-Fails if the argument theorem is not of the form {\small\verb%A |- tm = T%}.
-
-\SEEALSO
-EQT_INTRO, EQF_ELIM, EQF_INTRO.
-
-\ENDDOC
-\DOC{EQT\_INTRO}
-
-\TYPE {\small\verb%EQT_INTRO : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Introduces equality with {\small\verb%T%}.
-
-\DESCRIBE
-{\par\samepage\setseps\small
-\begin{verbatim}
-      A |- tm
-   -------------  EQF_INTRO
-    A |- tm = T
-\end{verbatim}
-}
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-EQT_ELIM, EQF_ELIM, EQF_INTRO.
-
-\ENDDOC
 \DOC{EQ\_IMP\_RULE}
 
 \TYPE {\small\verb%EQ_IMP_RULE : (thm -> (thm # thm))%}\egroup
@@ -6840,37 +6763,82 @@
 \end{verbatim}
 }
 \FAILURE
-Fails unless the first theorem is equational and its left side
-is the same as the conclusion of the second theorem (and is therefore
-of type {\small\verb%bool%}), up to alpha-conversion.
+Fails unless the first theorem is equational and its left side
+is the same as the conclusion of the second theorem (and is therefore
+of type {\small\verb%bool%}), up to alpha-conversion.
+
+\SEEALSO
+EQ_IMP_RULE, IMP_ANTISYM_RULE, MP.
+
+\ENDDOC
+\DOC{EQ\_TAC}
+
+\TYPE {\small\verb%EQ_TAC : tactic%}\egroup
+
+\SYNOPSIS
+Reduces goal of equality of boolean terms to forward and backward implication.
+
+\DESCRIBE
+When applied to a goal {\small\verb%A ?- t1 = t2%}, where {\small\verb%t1%} and {\small\verb%t2%} have type {\small\verb%bool%},
+the tactic {\small\verb%EQ_TAC%} returns the subgoals {\small\verb%A ?- t1 ==> t2%} and
+{\small\verb%A ?- t2 ==> t1%}.
+{\par\samepage\setseps\small
+\begin{verbatim}
+             A ?- t1 = t2
+   =================================  EQ_TAC
+    A ?- t1 ==> t2   A ?- t2 ==> t1
+\end{verbatim}
+}
+\FAILURE
+Fails unless the conclusion of the goal is an equation between boolean terms.
+
+\SEEALSO
+EQ_IMP_RULE, IMP_ANTISYM_RULE.
+
+\ENDDOC
+\DOC{EQT\_ELIM}
+
+\TYPE {\small\verb%EQT_ELIM : (thm -> thm)%}\egroup
+
+\SYNOPSIS
+Eliminates equality with {\small\verb%T%}.
+
+\DESCRIBE
+{\par\samepage\setseps\small
+\begin{verbatim}
+    A |- tm = T
+   -------------  EQT_ELIM
+      A |- tm
+\end{verbatim}
+}
+\FAILURE
+Fails if the argument theorem is not of the form {\small\verb%A |- tm = T%}.
 
 \SEEALSO
-EQ_IMP_RULE, IMP_ANTISYM_RULE, MP.
+EQT_INTRO, EQF_ELIM, EQF_INTRO.
 
 \ENDDOC
-\DOC{EQ\_TAC}
+\DOC{EQT\_INTRO}
 
-\TYPE {\small\verb%EQ_TAC : tactic%}\egroup
+\TYPE {\small\verb%EQT_INTRO : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Reduces goal of equality of boolean terms to forward and backward implication.
+Introduces equality with {\small\verb%T%}.
 
 \DESCRIBE
-When applied to a goal {\small\verb%A ?- t1 = t2%}, where {\small\verb%t1%} and {\small\verb%t2%} have type {\small\verb%bool%},
-the tactic {\small\verb%EQ_TAC%} returns the subgoals {\small\verb%A ?- t1 ==> t2%} and
-{\small\verb%A ?- t2 ==> t1%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-             A ?- t1 = t2
-   =================================  EQ_TAC
-    A ?- t1 ==> t2   A ?- t2 ==> t1
+      A |- tm
+   -------------  EQF_INTRO
+    A |- tm = T
 \end{verbatim}
 }
+
 \FAILURE
-Fails unless the conclusion of the goal is an equation between boolean terms.
+Never fails.
 
 \SEEALSO
-EQ_IMP_RULE, IMP_ANTISYM_RULE.
+EQT_ELIM, EQF_ELIM, EQF_INTRO.
 
 \ENDDOC
 \DOC{ETA\_CONV}
@@ -6888,37 +6856,6 @@
 Fails if the input term is not an eta-redex.
 
 \ENDDOC
-\DOC{EVERY}
-
-\TYPE {\small\verb%EVERY : (tactic list -> tactic)%}\egroup
-
-\SYNOPSIS
-Sequentially applies all the tactics in a given list of tactics.
-
-\DESCRIBE
-When applied to a list of tactics {\small\verb%[T1; ... ;Tn]%}, and a goal {\small\verb%g%}, the tactical
-{\small\verb%EVERY%} applies each tactic in sequence to every
-subgoal generated by the previous one. This can be represented as:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   EVERY [T1;...;Tn] = T1 THEN ... THEN Tn
-\end{verbatim}
-}
-\noindent If the tactic list is empty, the resulting tactic has no effect.
-
-\FAILURE
-The application of {\small\verb%EVERY%} to a tactic list never fails. The resulting
-tactic fails iff any of the component tactics do.
-
-\COMMENTS
-It is possible to use {\small\verb%EVERY%} instead of {\small\verb%THEN%}, but probably
-stylistically inferior. {\small\verb%EVERY%} is more useful when applied to a list of
-tactics generated by a function.
-
-\SEEALSO
-FIRST, MAP_EVERY, THEN.
-
-\ENDDOC
 \DOC{EVERY\_ASSUM}
 
 \TYPE {\small\verb%EVERY_ASSUM : (thm_tactic -> tactic)%}\egroup
@@ -6973,6 +6910,37 @@
 THENC.
 
 \ENDDOC
+\DOC{EVERY}
+
+\TYPE {\small\verb%EVERY : (tactic list -> tactic)%}\egroup
+
+\SYNOPSIS
+Sequentially applies all the tactics in a given list of tactics.
+
+\DESCRIBE
+When applied to a list of tactics {\small\verb%[T1; ... ;Tn]%}, and a goal {\small\verb%g%}, the tactical
+{\small\verb%EVERY%} applies each tactic in sequence to every
+subgoal generated by the previous one. This can be represented as:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   EVERY [T1;...;Tn] = T1 THEN ... THEN Tn
+\end{verbatim}
+}
+\noindent If the tactic list is empty, the resulting tactic has no effect.
+
+\FAILURE
+The application of {\small\verb%EVERY%} to a tactic list never fails. The resulting
+tactic fails iff any of the component tactics do.
+
+\COMMENTS
+It is possible to use {\small\verb%EVERY%} instead of {\small\verb%THEN%}, but probably
+stylistically inferior. {\small\verb%EVERY%} is more useful when applied to a list of
+tactics generated by a function.
+
+\SEEALSO
+FIRST, MAP_EVERY, THEN.
+
+\ENDDOC
 \DOC{EVERY\_TCL}
 
 \TYPE {\small\verb%EVERY_TCL : (thm_tactical list -> thm_tactical)%}\egroup
@@ -7035,43 +7003,43 @@
 EXISTS_UNIQUE_CONV.
 
 \ENDDOC
-\DOC{EXISTS}
+\DOC{EXISTS\_AND\_CONV}
 
-\TYPE {\small\verb%EXISTS : ((term # term) -> thm -> thm)%}\egroup
+\TYPE {\small\verb%EXISTS_AND_CONV : conv%}\egroup
 
 \SYNOPSIS
-Introduces existential quantification given a particular witness.
+Moves an existential quantification inwards through a conjunction.
 
 \DESCRIBE
-When applied to a pair of terms and a theorem, the first term an existentially
-quantified pattern indicating the desired form of the result, and the second a
-witness whose substitution for the quantified variable gives a term which is
-the same as the conclusion of the theorem, {\small\verb%EXISTS%} gives the desired theorem.
+When applied to a term of the form {\small\verb%?x. P /\ Q%}, where {\small\verb%x%} is not free in both
+{\small\verb%P%} and {\small\verb%Q%}, {\small\verb%EXISTS_AND_CONV%} returns a theorem of one of three forms,
+depending on occurrences of the variable {\small\verb%x%} in {\small\verb%P%} and {\small\verb%Q%}.  If {\small\verb%x%} is free
+in {\small\verb%P%} but not in {\small\verb%Q%}, then the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-    A |- p[u/x]
-   -------------  EXISTS ("?x. p","u")
-    A |- ?x. p
+   |- (?x. P /\ Q) = (?x.P) /\ Q
 \end{verbatim}
 }
-\FAILURE
-Fails unless the substituted pattern is the same as the conclusion of the
-theorem.
-
-\EXAMPLE
-The following examples illustrate how it is possible to deduce different
-things from the same theorem:
+\noindent is returned.  If {\small\verb%x%} is free in {\small\verb%Q%} but not in {\small\verb%P%}, then the
+result is:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #EXISTS ("?x. x=T","T") (REFL "T");;
-   |- ?x. x = T
-
-   #EXISTS ("?x:bool. x=x","T") (REFL "T");;
-   |- ?x. x = x
+   |- (?x. P /\ Q) = P /\ (?x.Q)
+\end{verbatim}
+}
+\noindent And if {\small\verb%x%} is free in neither {\small\verb%P%} nor {\small\verb%Q%}, then the result is:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- (?x. P /\ Q) = (?x.P) /\ (?x.Q)
 \end{verbatim}
 }
+\FAILURE
+{\small\verb%EXISTS_AND_CONV%} fails if it is applied to a term not of the form
+{\small\verb%?x. P /\ Q%}, or if it is applied to a term {\small\verb%?x. P /\ Q%} in which the
+variable {\small\verb%x%} is free in both {\small\verb%P%} and {\small\verb%Q%}.
+
 \SEEALSO
-CHOOSE, EXISTS_TAC.
+AND_EXISTS_CONV, LEFT_AND_EXISTS_CONV, RIGHT_AND_EXISTS_CONV.
 
 \ENDDOC
 \DOC{exists}
@@ -7093,43 +7061,43 @@
 forall, find, tryfind, mem, assoc, rev_assoc.
 
 \ENDDOC
-\DOC{EXISTS\_AND\_CONV}
+\DOC{EXISTS}
 
-\TYPE {\small\verb%EXISTS_AND_CONV : conv%}\egroup
+\TYPE {\small\verb%EXISTS : ((term # term) -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Moves an existential quantification inwards through a conjunction.
+Introduces existential quantification given a particular witness.
 
 \DESCRIBE
-When applied to a term of the form {\small\verb%?x. P /\ Q%}, where {\small\verb%x%} is not free in both
-{\small\verb%P%} and {\small\verb%Q%}, {\small\verb%EXISTS_AND_CONV%} returns a theorem of one of three forms,
-depending on occurrences of the variable {\small\verb%x%} in {\small\verb%P%} and {\small\verb%Q%}.  If {\small\verb%x%} is free
-in {\small\verb%P%} but not in {\small\verb%Q%}, then the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (?x. P /\ Q) = (?x.P) /\ Q
-\end{verbatim}
-}
-\noindent is returned.  If {\small\verb%x%} is free in {\small\verb%Q%} but not in {\small\verb%P%}, then the
-result is:
+When applied to a pair of terms and a theorem, the first term an existentially
+quantified pattern indicating the desired form of the result, and the second a
+witness whose substitution for the quantified variable gives a term which is
+the same as the conclusion of the theorem, {\small\verb%EXISTS%} gives the desired theorem.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (?x. P /\ Q) = P /\ (?x.Q)
+    A |- p[u/x]
+   -------------  EXISTS ("?x. p","u")
+    A |- ?x. p
 \end{verbatim}
 }
-\noindent And if {\small\verb%x%} is free in neither {\small\verb%P%} nor {\small\verb%Q%}, then the result is:
+\FAILURE
+Fails unless the substituted pattern is the same as the conclusion of the
+theorem.
+
+\EXAMPLE
+The following examples illustrate how it is possible to deduce different
+things from the same theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (?x. P /\ Q) = (?x.P) /\ (?x.Q)
+   #EXISTS ("?x. x=T","T") (REFL "T");;
+   |- ?x. x = T
+
+   #EXISTS ("?x:bool. x=x","T") (REFL "T");;
+   |- ?x. x = x
 \end{verbatim}
 }
-\FAILURE
-{\small\verb%EXISTS_AND_CONV%} fails if it is applied to a term not of the form
-{\small\verb%?x. P /\ Q%}, or if it is applied to a term {\small\verb%?x. P /\ Q%} in which the
-variable {\small\verb%x%} is free in both {\small\verb%P%} and {\small\verb%Q%}.
-
 \SEEALSO
-AND_EXISTS_CONV, LEFT_AND_EXISTS_CONV, RIGHT_AND_EXISTS_CONV.
+CHOOSE, EXISTS_TAC.
 
 \ENDDOC
 \DOC{EXISTS\_EQ}
@@ -7191,32 +7159,6 @@
 EXISTS_LEAST_CONV.
 
 \ENDDOC
-\DOC{EXISTS\_IMP}
-
-\TYPE {\small\verb%EXISTS_IMP : (term -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Existentially quantifies both the antecedent and consequent of an implication.
-
-\DESCRIBE
-When applied to a variable {\small\verb%x%} and a theorem {\small\verb%A |- t1 ==> t2%}, the
-inference rule {\small\verb%EXISTS_IMP%} returns the theorem {\small\verb%A |- (?x. t1) ==> (?x. t2)%},
-provided {\small\verb%x%} is not free in the assumptions.
-{\par\samepage\setseps\small
-\begin{verbatim}
-         A |- t1 ==> t2
-   --------------------------  EXISTS_IMP "x"   [where x is not free in A]
-    A |- (?x.t1) ==> (?x.t2)
-\end{verbatim}
-}
-\FAILURE
-Fails if the theorem is not implicative, or if the term is not a variable, or
-if the term is a variable but is free in the assumption list.
-
-\SEEALSO
-EXISTS_EQ.
-
-\ENDDOC
 \DOC{EXISTS\_IMP\_CONV}
 
 \TYPE {\small\verb%EXISTS_IMP_CONV : conv%}\egroup
@@ -7256,6 +7198,32 @@
 LEFT_IMP_FORALL_CONV, RIGHT_IMP_EXISTS_CONV.
 
 \ENDDOC
+\DOC{EXISTS\_IMP}
+
+\TYPE {\small\verb%EXISTS_IMP : (term -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Existentially quantifies both the antecedent and consequent of an implication.
+
+\DESCRIBE
+When applied to a variable {\small\verb%x%} and a theorem {\small\verb%A |- t1 ==> t2%}, the
+inference rule {\small\verb%EXISTS_IMP%} returns the theorem {\small\verb%A |- (?x. t1) ==> (?x. t2)%},
+provided {\small\verb%x%} is not free in the assumptions.
+{\par\samepage\setseps\small
+\begin{verbatim}
+         A |- t1 ==> t2
+   --------------------------  EXISTS_IMP "x"   [where x is not free in A]
+    A |- (?x.t1) ==> (?x.t2)
+\end{verbatim}
+}
+\FAILURE
+Fails if the theorem is not implicative, or if the term is not a variable, or
+if the term is a variable but is free in the assumption list.
+
+\SEEALSO
+EXISTS_EQ.
+
+\ENDDOC
 \DOC{EXISTS\_LEAST\_CONV}
 
 \TYPE {\small\verb%EXISTS_LEAST_CONV : conv%}\egroup
@@ -7779,30 +7747,12 @@
 \end{verbatim}
 }
 \COMMENTS
-This function is extremely dependent on the version of Lisp used, and its
-behaviour should not be relied upon; it may not work at all in Lisps other than
-Franz. It is questionable whether it is ever worthwhile to use it anyway,
-because although it cannot compromise the consistency of the logic, it can
-lead to confusing failures if one is manipulating numbers larger than the word
-size of the machine.
-
-\ENDDOC
-\DOC{filter}
-
-\TYPE {\small\verb%filter : ((* -> bool) -> * list -> * list)%}\egroup
-
-\SYNOPSIS
-Filters a list to the sublist of elements satisfying a predicate.
-
-\DESCRIBE
-{\small\verb%filter p l%} applies {\small\verb%p%} to every element of {\small\verb%l%}, returning a list of those
-that satisfy {\small\verb%p%}, in the order they appeared in the original list.
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-mapfilter, partition, remove.
+This function is extremely dependent on the version of Lisp used, and its
+behaviour should not be relied upon; it may not work at all in Lisps other than
+Franz. It is questionable whether it is ever worthwhile to use it anyway,
+because although it cannot compromise the consistency of the logic, it can
+lead to confusing failures if one is manipulating numbers larger than the word
+size of the machine.
 
 \ENDDOC
 \DOC{FILTER\_ASM\_REWRITE\_RULE}
@@ -8018,6 +7968,24 @@
 STRIP_TAC, UNDISCH, UNDISCH_ALL, UNDISCH_TAC.
 
 \ENDDOC
+\DOC{filter}
+
+\TYPE {\small\verb%filter : ((* -> bool) -> * list -> * list)%}\egroup
+
+\SYNOPSIS
+Filters a list to the sublist of elements satisfying a predicate.
+
+\DESCRIBE
+{\small\verb%filter p l%} applies {\small\verb%p%} to every element of {\small\verb%l%}, returning a list of those
+that satisfy {\small\verb%p%}, in the order they appeared in the original list.
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+mapfilter, partition, remove.
+
+\ENDDOC
 \DOC{FILTER\_GEN\_TAC}
 
 \TYPE {\small\verb%FILTER_GEN_TAC : (term -> tactic)%}\egroup
@@ -8587,61 +8555,6 @@
 find_file, find_ml_file, search_path, set_search_path.
 
 \ENDDOC
-\DOC{FIRST}
-
-\TYPE {\small\verb%FIRST : (tactic list -> tactic)%}\egroup
-
-\SYNOPSIS
-Applies the first tactic in a tactic list which succeeds.
-
-\DESCRIBE
-When applied to a list of tactics {\small\verb%[T1;...;Tn]%}, and a goal {\small\verb%g%}, the tactical
-{\small\verb%FIRST%} tries applying the tactics to the goal until one succeeds. If the
-first tactic which succeeds is {\small\verb%Tm%}, then the effect is the same as just {\small\verb%Tm%}.
-Thus {\small\verb%FIRST%} effectively behaves as follows:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   FIRST [T1;...;Tn] = T1 ORELSE ... ORELSE Tn
-\end{verbatim}
-}
-\FAILURE
-The application of {\small\verb%FIRST%} to a tactic list never fails. The resulting
-tactic fails iff all the component tactics do when applied to the goal,
-or if the tactic list is empty.
-
-\SEEALSO
-EVERY, ORELSE.
-
-\ENDDOC
-\DOC{FIRSTN\_CONV}
-
-\TYPE {\small\verb%FIRSTN_CONV : conv%}\egroup
-
-\SYNOPSIS
-Computes by inference the result of taking the initial n elements of a list.
-
-\DESCRIBE
-For any object language list of the form {\small\verb%"[x0;...x(n-k);...;x(n-1)]"%} ,
-the result of evaluating
-{\par\samepage\setseps\small
-\begin{verbatim}
-   FIRSTN_CONV "FIRSTN k [x0;...x(n-k);...;x(n-1)]"
-\end{verbatim}
-}
-\noindent is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- FIRSTN k [x0;...;x(n-k);...;x(n-1)] = [x0;...;x(n-k)]
-\end{verbatim}
-}
-
-
-\FAILURE
-{\small\verb%FIRSTN_CONV tm%} fails if {\small\verb%tm%} is not of the form described above, 
-or {\small\verb%k%} is greater than the length of the list.
-
-\ENDDOC
-
 \DOC{FIRST\_ASSUM}
 
 \TYPE {\small\verb%FIRST_ASSUM : (thm_tactic -> tactic)%}\egroup
@@ -8709,6 +8622,61 @@
 ORELSEC.
 
 \ENDDOC
+\DOC{FIRST}
+
+\TYPE {\small\verb%FIRST : (tactic list -> tactic)%}\egroup
+
+\SYNOPSIS
+Applies the first tactic in a tactic list which succeeds.
+
+\DESCRIBE
+When applied to a list of tactics {\small\verb%[T1;...;Tn]%}, and a goal {\small\verb%g%}, the tactical
+{\small\verb%FIRST%} tries applying the tactics to the goal until one succeeds. If the
+first tactic which succeeds is {\small\verb%Tm%}, then the effect is the same as just {\small\verb%Tm%}.
+Thus {\small\verb%FIRST%} effectively behaves as follows:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   FIRST [T1;...;Tn] = T1 ORELSE ... ORELSE Tn
+\end{verbatim}
+}
+\FAILURE
+The application of {\small\verb%FIRST%} to a tactic list never fails. The resulting
+tactic fails iff all the component tactics do when applied to the goal,
+or if the tactic list is empty.
+
+\SEEALSO
+EVERY, ORELSE.
+
+\ENDDOC
+\DOC{FIRSTN\_CONV}
+
+\TYPE {\small\verb%FIRSTN_CONV : conv%}\egroup
+
+\SYNOPSIS
+Computes by inference the result of taking the initial n elements of a list.
+
+\DESCRIBE
+For any object language list of the form {\small\verb%"[x0;...x(n-k);...;x(n-1)]"%} ,
+the result of evaluating
+{\par\samepage\setseps\small
+\begin{verbatim}
+   FIRSTN_CONV "FIRSTN k [x0;...x(n-k);...;x(n-1)]"
+\end{verbatim}
+}
+\noindent is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- FIRSTN k [x0;...;x(n-k);...;x(n-1)] = [x0;...;x(n-k)]
+\end{verbatim}
+}
+
+
+\FAILURE
+{\small\verb%FIRSTN_CONV tm%} fails if {\small\verb%tm%} is not of the form described above, 
+or {\small\verb%k%} is greater than the length of the list.
+
+\ENDDOC
+
 \DOC{FIRST\_TCL}
 
 \TYPE {\small\verb%FIRST_TCL : (thm_tactical list -> thm_tactical)%}\egroup
@@ -8752,28 +8720,6 @@
 set_flag.
 
 \ENDDOC
-\DOC{flat}
-
-\TYPE {\small\verb%flat : (* list list -> * list)%}\egroup
-
-\SYNOPSIS
-Flattens a list of lists into one long list.
-
-\DESCRIBE
-{\small\verb%flat [l1;...;ln]%} returns {\small\verb%(l1 @ ... @ ln)%} where each li is a list and {\small\verb%@%}
-is list concatenation.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#flat [[1;2];[3;4;5];[6]];;
-[1; 2; 3; 4; 5; 6] : int list
-\end{verbatim}
-}
-\ENDDOC
 \DOC{FLAT\_CONV}
 
 \TYPE {\small\verb%FLAT_CONV : conv%}\egroup
@@ -8819,6 +8765,28 @@
 
 \ENDDOC
 
+\DOC{flat}
+
+\TYPE {\small\verb%flat : (* list list -> * list)%}\egroup
+
+\SYNOPSIS
+Flattens a list of lists into one long list.
+
+\DESCRIBE
+{\small\verb%flat [l1;...;ln]%} returns {\small\verb%(l1 @ ... @ ln)%} where each li is a list and {\small\verb%@%}
+is list concatenation.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#flat [[1;2];[3;4;5];[6]];;
+[1; 2; 3; 4; 5; 6] : int list
+\end{verbatim}
+}
+\ENDDOC
 \DOC{FOLDL\_CONV}
 
 \TYPE {\small\verb%FOLDL_CONV : conv -> conv%}\egroup
@@ -8953,25 +8921,6 @@
 
 \ENDDOC
 
-\DOC{forall}
-
-\TYPE {\small\verb%forall : ((* -> bool) -> * list -> bool)%}\egroup
-
-\SYNOPSIS
-Tests a list to see if all its elements satisfy a predicate.
-
-\DESCRIBE
-{\small\verb%forall p [x1;...;xn]%} returns {\small\verb%true%} if {\small\verb%(p xi)%} is true for all {\small\verb%xi%} in the
-list. Otherwise it returns {\small\verb%false%}. If the list is empty, this function always
-returns true.
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-exists, find, tryfind, mem, assoc, rev_assoc.
-
-\ENDDOC
 \DOC{FORALL\_AND\_CONV}
 
 \TYPE {\small\verb%FORALL_AND_CONV : conv%}\egroup
@@ -8994,6 +8943,25 @@
 AND_FORALL_CONV, LEFT_AND_FORALL_CONV, RIGHT_AND_FORALL_CONV.
 
 \ENDDOC
+\DOC{forall}
+
+\TYPE {\small\verb%forall : ((* -> bool) -> * list -> bool)%}\egroup
+
+\SYNOPSIS
+Tests a list to see if all its elements satisfy a predicate.
+
+\DESCRIBE
+{\small\verb%forall p [x1;...;xn]%} returns {\small\verb%true%} if {\small\verb%(p xi)%} is true for all {\small\verb%xi%} in the
+list. Otherwise it returns {\small\verb%false%}. If the list is empty, this function always
+returns true.
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+exists, find, tryfind, mem, assoc, rev_assoc.
+
+\ENDDOC
 \DOC{FORALL\_EQ}
 
 \TYPE {\small\verb%FORALL_EQ : (term -> thm -> thm)%}\egroup
@@ -9113,13 +9081,49 @@
    |- (!x. P \/ Q) = (!x.P) \/ (!x.Q)
 \end{verbatim}
 }
-\FAILURE
-{\small\verb%FORALL_OR_CONV%} fails if it is applied to a term not of the form
-{\small\verb%!x. P \/ Q%}, or if it is applied to a term {\small\verb%!x. P \/ Q%} in which the
-variable {\small\verb%x%} is free in both {\small\verb%P%} and {\small\verb%Q%}.
-
+\FAILURE
+{\small\verb%FORALL_OR_CONV%} fails if it is applied to a term not of the form
+{\small\verb%!x. P \/ Q%}, or if it is applied to a term {\small\verb%!x. P \/ Q%} in which the
+variable {\small\verb%x%} is free in both {\small\verb%P%} and {\small\verb%Q%}.
+
+\SEEALSO
+OR_FORALL_CONV, LEFT_OR_FORALL_CONV, RIGHT_OR_FORALL_CONV.
+
+\ENDDOC
+\DOC{free\_in}
+
+\TYPE {\small\verb%free_in : (term -> term -> bool)%}\egroup
+
+\SYNOPSIS
+Tests if one term is free in another.
+
+\DESCRIBE
+When applied to two terms {\small\verb%t1%} and {\small\verb%t2%}, the function {\small\verb%free_in%} returns
+{\small\verb%true%} if {\small\verb%t1%} is free in {\small\verb%t2%}, and {\small\verb%false%} otherwise. It is not necessary
+that {\small\verb%t1%} be simply a variable.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+In the following example {\small\verb%free_in%} returns {\small\verb%false%} because the {\small\verb%x%} in {\small\verb%SUC x%}
+in the second term is bound:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #free_in "SUC x" "!x. SUC x = x + 1";;
+   false : bool
+\end{verbatim}
+}
+\noindent whereas the following call returns {\small\verb%true%} because the first instance
+of {\small\verb%x%} in the second term is free, even though there is also a bound instance:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #free_in "x:bool" "x /\ (?x. x=T)";;
+   true : bool
+\end{verbatim}
+}
 \SEEALSO
-OR_FORALL_CONV, LEFT_OR_FORALL_CONV, RIGHT_OR_FORALL_CONV.
+frees, freesl, thm_frees.
 
 \ENDDOC
 \DOC{frees}
@@ -9250,42 +9254,6 @@
 ASSUME, IMP_RES_TAC, PROVE_HYP, RES_TAC, REWR_CONV.
 
 \ENDDOC
-\DOC{free\_in}
-
-\TYPE {\small\verb%free_in : (term -> term -> bool)%}\egroup
-
-\SYNOPSIS
-Tests if one term is free in another.
-
-\DESCRIBE
-When applied to two terms {\small\verb%t1%} and {\small\verb%t2%}, the function {\small\verb%free_in%} returns
-{\small\verb%true%} if {\small\verb%t1%} is free in {\small\verb%t2%}, and {\small\verb%false%} otherwise. It is not necessary
-that {\small\verb%t1%} be simply a variable.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-In the following example {\small\verb%free_in%} returns {\small\verb%false%} because the {\small\verb%x%} in {\small\verb%SUC x%}
-in the second term is bound:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #free_in "SUC x" "!x. SUC x = x + 1";;
-   false : bool
-\end{verbatim}
-}
-\noindent whereas the following call returns {\small\verb%true%} because the first instance
-of {\small\verb%x%} in the second term is free, even though there is also a bound instance:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #free_in "x:bool" "x /\ (?x. x=T)";;
-   true : bool
-\end{verbatim}
-}
-\SEEALSO
-frees, freesl, thm_frees.
-
-\ENDDOC
 \DOC{FRONT\_CONJ\_CONV}
 
 \TYPE {\small\verb%FRONT_CONJ_CONV: (term list -> term -> thm)%}\egroup
@@ -9330,6 +9298,36 @@
 snd, pair.
 
 \ENDDOC
+\DOC{FUN\_EQ\_CONV}
+
+\TYPE {\small\verb%FUN_EQ_CONV : conv%}\egroup
+
+\SYNOPSIS
+Equates normal and extensional equality for two functions.
+
+\DESCRIBE
+The conversion {\small\verb%FUN_EQ_CONV%} embodies the fact that two functions are equal
+precisely when they give the same results for all values to which they can be
+applied. When supplied with a term argument of the form {\small\verb%f = g%}, where {\small\verb%f%} and
+{\small\verb%g%} are functions of type {\small\verb%ty1->ty2%}, {\small\verb%FUN_EQ_CONV%} returns the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- (f = g) = (!x. f x = g x)
+\end{verbatim}
+}
+\noindent where {\small\verb%x%} is a variable of type {\small\verb%ty1%} chosen by the conversion.
+
+\FAILURE
+{\small\verb%FUN_EQ_CONV tm%} fails if {\small\verb%tm%} is not an equation {\small\verb%f = g%}, where {\small\verb%f%} and {\small\verb%g%}
+are functions.
+
+\USES
+Used for proving equality of functions.
+
+\SEEALSO
+EXT, X_FUN_EQ_CONV.
+
+\ENDDOC
 \DOC{funpow}
 
 \TYPE {\small\verb%funpow : (int -> (* -> *) -> * -> *)%}\egroup
@@ -9384,36 +9382,6 @@
 \end{verbatim}
 }
 \ENDDOC
-\DOC{FUN\_EQ\_CONV}
-
-\TYPE {\small\verb%FUN_EQ_CONV : conv%}\egroup
-
-\SYNOPSIS
-Equates normal and extensional equality for two functions.
-
-\DESCRIBE
-The conversion {\small\verb%FUN_EQ_CONV%} embodies the fact that two functions are equal
-precisely when they give the same results for all values to which they can be
-applied. When supplied with a term argument of the form {\small\verb%f = g%}, where {\small\verb%f%} and
-{\small\verb%g%} are functions of type {\small\verb%ty1->ty2%}, {\small\verb%FUN_EQ_CONV%} returns the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (f = g) = (!x. f x = g x)
-\end{verbatim}
-}
-\noindent where {\small\verb%x%} is a variable of type {\small\verb%ty1%} chosen by the conversion.
-
-\FAILURE
-{\small\verb%FUN_EQ_CONV tm%} fails if {\small\verb%tm%} is not an equation {\small\verb%f = g%}, where {\small\verb%f%} and {\small\verb%g%}
-are functions.
-
-\USES
-Used for proving equality of functions.
-
-\SEEALSO
-EXT, X_FUN_EQ_CONV.
-
-\ENDDOC
 \DOC{g}
 
 \TYPE {\small\verb%g : (term -> void)%}\egroup
@@ -9454,120 +9422,6 @@
 rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
 
 \ENDDOC
-\DOC{GEN}
-
-\TYPE {\small\verb%GEN : (term -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Generalizes the conclusion of a theorem.
-
-\DESCRIBE
-When applied to a term {\small\verb%x%} and a theorem {\small\verb%A |- t%}, the inference rule
-{\small\verb%GEN%} returns the theorem {\small\verb%A |- !x. t%}, provided {\small\verb%x%} is a variable not
-free in any of the assumptions. There is no compulsion that {\small\verb%x%} should
-be free in {\small\verb%t%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-      A |- t
-   ------------  GEN "x"                [where x is not free in A]
-    A |- !x. t
-\end{verbatim}
-}
-\FAILURE
-Fails if {\small\verb%x%} is not a variable, or if it is free in any of the assumptions.
-
-\EXAMPLE
-The following example shows how the above side-condition prevents
-the derivation of the theorem {\small\verb%x=T |- !x. x=T%}, which is clearly invalid.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #top_print print_all_thm;;
-   - : (thm -> void)
-
-   #let t = ASSUME "x=T";;
-   t = x = T |- x = T
-
-   #GEN "x:bool" t;;
-   evaluation failed     GEN
-\end{verbatim}
-}
-\SEEALSO
-GENL, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
-
-\ENDDOC
-\DOC{GENL}
-
-\TYPE {\small\verb%GENL : (term list -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Generalizes zero or more variables in the conclusion of a theorem.
-
-\DESCRIBE
-When applied to a term list {\small\verb%[x1;...;xn]%} and a theorem {\small\verb%A |- t%}, the inference
-rule {\small\verb%GENL%} returns the theorem {\small\verb%A |- !x1...xn. t%}, provided none of the
-variables {\small\verb%xi%} are free in any of the assumptions. It is not necessary that
-any or all of the {\small\verb%xi%} should be free in {\small\verb%t%}.
-{\par\samepage\setseps\small
-\begin{verbatim}
-         A |- t
-   ------------------  GENL "[x1;...;xn]"       [where no xi is free in A]
-    A |- !x1...xn. t
-\end{verbatim}
-}
-\FAILURE
-Fails unless all the terms in the list are variables, none of which are
-free in the assumption list.
-
-\SEEALSO
-GEN, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
-
-\ENDDOC
-\DOC{genvar}
-
-\TYPE {\small\verb%genvar : (type -> term)%}\egroup
-
-\SYNOPSIS
-Returns a variable whose name has not been used previously.
-
-\DESCRIBE
-When given a type, {\small\verb%genvar%} returns a variable of that type whose name has
-not been used for a variable or constant in the HOL session so far.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-The following indicates the typical stylized form of the names (this should
-not be relied on, of course):
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #genvar ":bool";;
-   "GEN%VAR%357" : term
-
-   #genvar ":num";;
-   "GEN%VAR%358" : term
-\end{verbatim}
-}
-\noindent Trying to anticipate {\small\verb%genvar%} doesn't work:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #let v = mk_var(`GEN%VAR%359`,":bool");;
-   v = "GEN%VAR%359" : term
-
-   #genvar ":bool";;
-   "GEN%VAR%360" : term
-\end{verbatim}
-}
-\USES
-The unique variables are useful in writing derived rules, for specializing
-terms without having to worry about such things as free variable capture.
-If the names are to be visible to a typical user, the function {\small\verb%variant%} can
-provide rather more meaningful names.
-
-\SEEALSO
-GSPEC, variant.
-
-\ENDDOC
 \DOC{GEN\_ALL}
 
 \TYPE {\small\verb%GEN_ALL : (thm -> thm)%}\egroup
@@ -9670,21 +9524,89 @@
 pair, so {\small\verb%FST%} and {\small\verb%SND%} are introduced:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #GEN_BETA_CONV "(\(x,y). x + y) numpair";;
-   |- (\(x,y). x + y)numpair = (FST numpair) + (SND numpair)
+   #GEN_BETA_CONV "(\(x,y). x + y) numpair";;
+   |- (\(x,y). x + y)numpair = (FST numpair) + (SND numpair)
+\end{verbatim}
+}
+\noindent The introduction of {\small\verb%FST%} and {\small\verb%SND%} will be done more than once as
+necessary:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #GEN_BETA_CONV "(\(w,x,y,z). w + x + y + z) (1,triple)";;
+   |- (\(w,x,y,z). w + (x + (y + z)))(1,triple) =
+      1 + ((FST triple) + ((FST(SND triple)) + (SND(SND triple))))
+\end{verbatim}
+}
+\SEEALSO
+BETA_CONV, PAIRED_BETA_CONV.
+
+\ENDDOC
+\DOC{GEN}
+
+\TYPE {\small\verb%GEN : (term -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Generalizes the conclusion of a theorem.
+
+\DESCRIBE
+When applied to a term {\small\verb%x%} and a theorem {\small\verb%A |- t%}, the inference rule
+{\small\verb%GEN%} returns the theorem {\small\verb%A |- !x. t%}, provided {\small\verb%x%} is a variable not
+free in any of the assumptions. There is no compulsion that {\small\verb%x%} should
+be free in {\small\verb%t%}.
+{\par\samepage\setseps\small
+\begin{verbatim}
+      A |- t
+   ------------  GEN "x"                [where x is not free in A]
+    A |- !x. t
+\end{verbatim}
+}
+\FAILURE
+Fails if {\small\verb%x%} is not a variable, or if it is free in any of the assumptions.
+
+\EXAMPLE
+The following example shows how the above side-condition prevents
+the derivation of the theorem {\small\verb%x=T |- !x. x=T%}, which is clearly invalid.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #top_print print_all_thm;;
+   - : (thm -> void)
+
+   #let t = ASSUME "x=T";;
+   t = x = T |- x = T
+
+   #GEN "x:bool" t;;
+   evaluation failed     GEN
 \end{verbatim}
 }
-\noindent The introduction of {\small\verb%FST%} and {\small\verb%SND%} will be done more than once as
-necessary:
+\SEEALSO
+GENL, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
+
+\ENDDOC
+\DOC{GENL}
+
+\TYPE {\small\verb%GENL : (term list -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Generalizes zero or more variables in the conclusion of a theorem.
+
+\DESCRIBE
+When applied to a term list {\small\verb%[x1;...;xn]%} and a theorem {\small\verb%A |- t%}, the inference
+rule {\small\verb%GENL%} returns the theorem {\small\verb%A |- !x1...xn. t%}, provided none of the
+variables {\small\verb%xi%} are free in any of the assumptions. It is not necessary that
+any or all of the {\small\verb%xi%} should be free in {\small\verb%t%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #GEN_BETA_CONV "(\(w,x,y,z). w + x + y + z) (1,triple)";;
-   |- (\(w,x,y,z). w + (x + (y + z)))(1,triple) =
-      1 + ((FST triple) + ((FST(SND triple)) + (SND(SND triple))))
+         A |- t
+   ------------------  GENL "[x1;...;xn]"       [where no xi is free in A]
+    A |- !x1...xn. t
 \end{verbatim}
 }
+\FAILURE
+Fails unless all the terms in the list are variables, none of which are
+free in the assumption list.
+
 \SEEALSO
-BETA_CONV, PAIRED_BETA_CONV.
+GEN, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
 
 \ENDDOC
 \DOC{GEN\_REWRITE\_CONV}
@@ -9976,28 +9898,51 @@
 X_GEN_TAC.
 
 \ENDDOC
-\DOC{getenv}
+\DOC{genvar}
 
-\TYPE {\small\verb%getenv : (string -> string)%}\egroup
+\TYPE {\small\verb%genvar : (type -> term)%}\egroup
 
 \SYNOPSIS
-Returns the value of a Unix environment variable.
+Returns a variable whose name has not been used previously.
 
 \DESCRIBE
-{\small\verb%getenv x%} returns the value of {\small\verb%x%} from the current environment list; this
-will include shell environment variables set before {\small\verb%HOL%} is run.
+When given a type, {\small\verb%genvar%} returns a variable of that type whose name has
+not been used for a variable or constant in the HOL session so far.
 
 \FAILURE
-If in a Unix environment, fails with {\small\verb%getenv%} if the variable is undefined,
-or has an empty value. In other environments, it will normally fail anyway.
+Never fails.
 
 \EXAMPLE
+The following indicates the typical stylized form of the names (this should
+not be relied on, of course):
 {\par\samepage\setseps\small
 \begin{verbatim}
-#getenv `SHELL`;;
-`/bin/csh` : string
+   #genvar ":bool";;
+   "GEN%VAR%357" : term
+
+   #genvar ":num";;
+   "GEN%VAR%358" : term
+\end{verbatim}
+}
+\noindent Trying to anticipate {\small\verb%genvar%} doesn't work:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #let v = mk_var(`GEN%VAR%359`,":bool");;
+   v = "GEN%VAR%359" : term
+
+   #genvar ":bool";;
+   "GEN%VAR%360" : term
 \end{verbatim}
 }
+\USES
+The unique variables are useful in writing derived rules, for specializing
+terms without having to worry about such things as free variable capture.
+If the names are to be visible to a typical user, the function {\small\verb%variant%} can
+provide rather more meaningful names.
+
+\SEEALSO
+GSPEC, variant.
+
 \ENDDOC
 \DOC{get\_const\_type}
 
@@ -10023,6 +9968,29 @@
 dest_const, is_constant.
 
 \ENDDOC
+\DOC{getenv}
+
+\TYPE {\small\verb%getenv : (string -> string)%}\egroup
+
+\SYNOPSIS
+Returns the value of a Unix environment variable.
+
+\DESCRIBE
+{\small\verb%getenv x%} returns the value of {\small\verb%x%} from the current environment list; this
+will include shell environment variables set before {\small\verb%HOL%} is run.
+
+\FAILURE
+If in a Unix environment, fails with {\small\verb%getenv%} if the variable is undefined,
+or has an empty value. In other environments, it will normally fail anyway.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#getenv `SHELL`;;
+`/bin/csh` : string
+\end{verbatim}
+}
+\ENDDOC
 \DOC{get\_flag\_value}
 
 \TYPE {\small\verb%get_flag_value : (string -> bool)%}\egroup
@@ -10330,6 +10298,36 @@
 ETA_CONV, MK_ABS, MK_COMB, MK_EXISTS.
 
 \ENDDOC
+\DOC{\char'136}
+
+\TYPE {\small\verb%$^ : (string -> string -> string)%}\egroup
+
+\SYNOPSIS
+Concatenates two ML strings.
+
+\DESCRIBE
+The {\small\verb%^%} is the ML infix string concatenation operator.
+If {\small\verb%s1%} and {\small\verb%s2%} are strings, then {\small\verb%s1^s2%} gives a string which is their
+concatenation.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#`Hello `^`world`;;
+`Hello world` : string
+\end{verbatim}
+}
+\COMMENTS
+The ML role of the {\small\verb%^%} operator should not be confused with its use in
+quoted terms to introduce antiquotation (see DESCRIPTION for details).
+
+\SEEALSO
+concat, concatl.
+
+\ENDDOC
 \DOC{hd}
 
 \TYPE {\small\verb%hd : (* list -> *)%}\egroup
@@ -10544,36 +10542,6 @@
 \#, B, C, CB, Co, K, KI, o, oo, S, W.
 
 \ENDDOC
-\DOC{implode}
-
-\TYPE {\small\verb%implode : (string list -> string)%}\egroup
-
-\SYNOPSIS
-Converts a list of single-character strings into one string.
-
-\DESCRIBE
-{\small\verb%implode [s1;...;sn]%} returns the string formed by concatenating the
-single-character strings {\small\verb%s1 ... sn%}. If {\small\verb%n%} is zero (the list is empty),
-then the empty string is returned.
-
-\FAILURE
-Fails if any of the strings in the argument list are null or longer than one
-character.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#implode [`e`;`x`;`a`;`m`;`p`;`l`;`e`];;
-`example` : string
-
-#implode [`ex`;`a`;`mpl`;``;`e`];;
-evaluation failed     implode
-\end{verbatim}
-}
-\SEEALSO
-explode, concat, concatl.
-
-\ENDDOC
 \DOC{IMP\_ANTISYM\_RULE}
 
 \TYPE {\small\verb%IMP_ANTISYM_RULE : (thm -> thm -> thm)%}\egroup
@@ -10680,6 +10648,36 @@
 NOT_INTRO, NOT_ELIM.
 
 \ENDDOC
+\DOC{implode}
+
+\TYPE {\small\verb%implode : (string list -> string)%}\egroup
+
+\SYNOPSIS
+Converts a list of single-character strings into one string.
+
+\DESCRIBE
+{\small\verb%implode [s1;...;sn]%} returns the string formed by concatenating the
+single-character strings {\small\verb%s1 ... sn%}. If {\small\verb%n%} is zero (the list is empty),
+then the empty string is returned.
+
+\FAILURE
+Fails if any of the strings in the argument list are null or longer than one
+character.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#implode [`e`;`x`;`a`;`m`;`p`;`l`;`e`];;
+`example` : string
+
+#implode [`ex`;`a`;`mpl`;``;`e`];;
+evaluation failed     implode
+\end{verbatim}
+}
+\SEEALSO
+explode, concat, concatl.
+
+\ENDDOC
 \DOC{IMP\_RES\_TAC}
 
 \TYPE {\small\verb%IMP_RES_TAC : thm_tactic%}\egroup
@@ -11193,43 +11191,73 @@
 inl, isl, outl, outr.
 
 \ENDDOC
-\DOC{INST}
+\DOC{install}
 
-\TYPE {\small\verb%INST : ((term # term) list -> thm -> thm)%}\egroup
+\TYPE {\small\verb%install : (string -> void)%}\egroup
 
 \SYNOPSIS
-Instantiates free variables in a theorem.
+Informs HOL of the absolute pathname to the hol distribution directory.
 
 \DESCRIBE
-{\small\verb%INST%} is a rule for substituting arbitrary terms for free variables
-in a theorem:
+{\small\verb%install%} reconfigures a running HOL system to a new root directory.  The
+string argument to {\small\verb%install%} should be the absolute path name to the
+directory in which the HOL system is located. Executing
 {\par\samepage\setseps\small
 \begin{verbatim}
-             A |- t
-   -----------------------------  INST [(t1,x1);...;(tn,xn)]
-    A |- t[t1,...,tn/x1,...,xn]
+   install `/dir1/dir2/dir3/.../hol`;;
 \end{verbatim}
 }
-\noindent where the variables {\small\verb%x1, ..., xn%} are not free in the
-assumptions {\small\verb%A%}.
+\noindent sets the internal HOL search path to:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   [``; `~/`; `/dir1/dir2/dir3/.../hol/theories/`]
+\end{verbatim}
+}
+\noindent In addition, {\small\verb%install%} sets the internal search path used by HOL to
+find the standard online help files and the internal search path used by HOL to
+find libraries.
 
 \FAILURE
-{\small\verb%INST%} fails if a variable being instantiated is free in the
-assumptions.
+Never fails.
 
-\EXAMPLE
-In the following example a theorem is instantiated for a specific term:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #CONJUNCT1 ADD_CLAUSES ;;
-   |- 0 + m = m
+\COMMENTS
+The effect persists only for the current HOL session. To change the image
+permanently, use the {\small\verb%save%} function after installation.
 
-   #INST [("2 * x","m:num")] (CONJUNCT1 ADD_CLAUSES) ;;
-   |- 0 + (2 * x) = 2 * x
+\SEEALSO
+help_search_path, library_pathname, library_search_path, search_path,
+set_help_search_path, set_library_search_path, set_search_path.
+
+\ENDDOC
+\DOC{inst\_check}
+
+\TYPE {\small\verb%inst_check : (((type # type) list # term list) -> term list)%}\egroup
+
+\SYNOPSIS
+Checks the validity of type instantiations.
+
+\DESCRIBE
+If the {\small\verb%t1...tn%} are types (monomorphic or polymorphic), the {\small\verb%v1...vn%} type
+variables (e.g. {\small\verb%":*"%}), and {\small\verb%tm1...tmn%} terms, the call
+{\par\samepage\setseps\small
+\begin{verbatim}
+   inst_check ([(t1,v1);...;(tn,vn)],[tm1;...;tmn])
 \end{verbatim}
 }
+\noindent will return a list of the variables free in the {\small\verb%tm1...tmn%}, provided
+none of the type variables {\small\verb%v1...vn%} are free in {\small\verb%tm1...tmn%}. If this condition
+is not met, or any of the {\small\verb%v%}'s are not simply type variables, the call fails.
+
+\FAILURE
+Fails if any of the {\small\verb%v%}'s are not simple type variables, or if any of them are
+free in the terms {\small\verb%v1...vn%}.
+
+\USES
+Checking the validity of type instantiations (for example, if the terms are the
+hypotheses of a theorem).
+
 \SEEALSO
-INST_TY_TERM, INST_TYPE, ISPEC, ISPECL, SPEC; SPECL, SUBS, subst, SUBST.
+inst, inst_rename_list, inst_type, INST_TYPE.
 
 \ENDDOC
 \DOC{inst}
@@ -11281,73 +11309,43 @@
 inst_check, inst_rename_list, inst_type, INST_TYPE.
 
 \ENDDOC
-\DOC{install}
+\DOC{INST}
 
-\TYPE {\small\verb%install : (string -> void)%}\egroup
+\TYPE {\small\verb%INST : ((term # term) list -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Informs HOL of the absolute pathname to the hol distribution directory.
+Instantiates free variables in a theorem.
 
 \DESCRIBE
-{\small\verb%install%} reconfigures a running HOL system to a new root directory.  The
-string argument to {\small\verb%install%} should be the absolute path name to the
-directory in which the HOL system is located. Executing
-{\par\samepage\setseps\small
-\begin{verbatim}
-   install `/dir1/dir2/dir3/.../hol`;;
-\end{verbatim}
-}
-\noindent sets the internal HOL search path to:
+{\small\verb%INST%} is a rule for substituting arbitrary terms for free variables
+in a theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   [``; `~/`; `/dir1/dir2/dir3/.../hol/theories/`]
+             A |- t
+   -----------------------------  INST [(t1,x1);...;(tn,xn)]
+    A |- t[t1,...,tn/x1,...,xn]
 \end{verbatim}
 }
-\noindent In addition, {\small\verb%install%} sets the internal search path used by HOL to
-find the standard online help files and the internal search path used by HOL to
-find libraries.
+\noindent where the variables {\small\verb%x1, ..., xn%} are not free in the
+assumptions {\small\verb%A%}.
 
 \FAILURE
-Never fails.
-
-\COMMENTS
-The effect persists only for the current HOL session. To change the image
-permanently, use the {\small\verb%save%} function after installation.
-
-\SEEALSO
-help_search_path, library_pathname, library_search_path, search_path,
-set_help_search_path, set_library_search_path, set_search_path.
-
-\ENDDOC
-\DOC{inst\_check}
-
-\TYPE {\small\verb%inst_check : (((type # type) list # term list) -> term list)%}\egroup
-
-\SYNOPSIS
-Checks the validity of type instantiations.
+{\small\verb%INST%} fails if a variable being instantiated is free in the
+assumptions.
 
-\DESCRIBE
-If the {\small\verb%t1...tn%} are types (monomorphic or polymorphic), the {\small\verb%v1...vn%} type
-variables (e.g. {\small\verb%":*"%}), and {\small\verb%tm1...tmn%} terms, the call
+\EXAMPLE
+In the following example a theorem is instantiated for a specific term:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   inst_check ([(t1,v1);...;(tn,vn)],[tm1;...;tmn])
+   #CONJUNCT1 ADD_CLAUSES ;;
+   |- 0 + m = m
+
+   #INST [("2 * x","m:num")] (CONJUNCT1 ADD_CLAUSES) ;;
+   |- 0 + (2 * x) = 2 * x
 \end{verbatim}
 }
-\noindent will return a list of the variables free in the {\small\verb%tm1...tmn%}, provided
-none of the type variables {\small\verb%v1...vn%} are free in {\small\verb%tm1...tmn%}. If this condition
-is not met, or any of the {\small\verb%v%}'s are not simply type variables, the call fails.
-
-\FAILURE
-Fails if any of the {\small\verb%v%}'s are not simple type variables, or if any of them are
-free in the terms {\small\verb%v1...vn%}.
-
-\USES
-Checking the validity of type instantiations (for example, if the terms are the
-hypotheses of a theorem).
-
 \SEEALSO
-inst, inst_rename_list, inst_type, INST_TYPE.
+INST_TY_TERM, INST_TYPE, ISPEC, ISPECL, SPEC; SPECL, SUBS, subst, SUBST.
 
 \ENDDOC
 \DOC{inst\_rename\_list}
@@ -11395,6 +11393,51 @@
 inst, inst_check, inst_type, INST_TYPE.
 
 \ENDDOC
+\DOC{inst\_type}
+
+\TYPE {\small\verb%inst_type : ((type # type) list -> type -> type)%}\egroup
+
+\SYNOPSIS
+Instantiates types in a type.
+
+\DESCRIBE
+If {\small\verb%[(t1',t1);...;(tn',tn)]%} is a list of type instantiations, where {\small\verb%t1...tn%}
+are the initial types, and {\small\verb%t1'...tn'%} the desired instantiations, and {\small\verb%ty%} is
+a type to instantiate, the call
+{\par\samepage\setseps\small
+\begin{verbatim}
+   inst_type [(t1',t1);...;(tn',tn)] ty
+\end{verbatim}
+}
+\noindent will appropriately instantiate the type {\small\verb%ty%}. The instantiations will
+be performed in parallel. If several of the type instantiations are applicable,
+the choice is undefined. In normal use the {\small\verb%t1...tn%} are type variables,
+although this is not essential. Neither is it necessary that any or all of the
+types {\small\verb%t1...tn%} should in fact appear in {\small\verb%ty%}.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#inst_type [(":bool",":*")] ":* # **";;
+":bool # **" : type
+
+#inst_type [(":num",":* # **"); (":bool",":*")] ":* # **";;
+":num" : type
+
+#inst_type [(":bool",":*"); (":num",":* # **")] ":* # **";;
+":num" : type
+
+#inst_type [(":bool",":num"); (":num",":bool")] ":(bool)list";;
+":(num)list" : type
+\end{verbatim}
+}
+\SEEALSO
+inst, inst_check, inst_type, INST_TYPE.
+
+\ENDDOC
 \DOC{INST\_TYPE}
 
 \TYPE {\small\verb%INST_TYPE : ((type # type) list -> thm -> thm)%}\egroup
@@ -11446,51 +11489,6 @@
 INST, INST_TY_TERM.
 
 \ENDDOC
-\DOC{inst\_type}
-
-\TYPE {\small\verb%inst_type : ((type # type) list -> type -> type)%}\egroup
-
-\SYNOPSIS
-Instantiates types in a type.
-
-\DESCRIBE
-If {\small\verb%[(t1',t1);...;(tn',tn)]%} is a list of type instantiations, where {\small\verb%t1...tn%}
-are the initial types, and {\small\verb%t1'...tn'%} the desired instantiations, and {\small\verb%ty%} is
-a type to instantiate, the call
-{\par\samepage\setseps\small
-\begin{verbatim}
-   inst_type [(t1',t1);...;(tn',tn)] ty
-\end{verbatim}
-}
-\noindent will appropriately instantiate the type {\small\verb%ty%}. The instantiations will
-be performed in parallel. If several of the type instantiations are applicable,
-the choice is undefined. In normal use the {\small\verb%t1...tn%} are type variables,
-although this is not essential. Neither is it necessary that any or all of the
-types {\small\verb%t1...tn%} should in fact appear in {\small\verb%ty%}.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#inst_type [(":bool",":*")] ":* # **";;
-":bool # **" : type
-
-#inst_type [(":num",":* # **"); (":bool",":*")] ":* # **";;
-":num" : type
-
-#inst_type [(":bool",":*"); (":num",":* # **")] ":* # **";;
-":num" : type
-
-#inst_type [(":bool",":num"); (":num",":bool")] ":(bool)list";;
-":(num)list" : type
-\end{verbatim}
-}
-\SEEALSO
-inst, inst_check, inst_type, INST_TYPE.
-
-\ENDDOC
 \DOC{INST\_TY\_TERM}
 
 \TYPE {\small\verb%INST_TY_TERM : (((term # term) list # (type # type) list) -> thm -> thm)%}\egroup
@@ -11583,105 +11581,25 @@
 \TYPE {\small\verb%int_of_term : (term -> int)%}\egroup
 
 \SYNOPSIS
-Maps a numeric term to the corresponding ML integer.
-
-\DESCRIBE
-Given a term representing a natural number, i.e., of type {\small\verb%:num%}
-{\small\verb%int_of_term%} returns the corresponding ML integer constant.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #int_of_term "2";;
-   2 : int
-\end{verbatim}
-}
-
-\SEEALSO
-term_of_int, string_of_int, int_of_string.
-
-\ENDDOC
-\DOC{isl}
-
-\TYPE {\small\verb%isl : ((* + **) -> bool)%}\egroup
-
-\SYNOPSIS
-Tests for membership of left summand.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#let x = inl 1 and y = inr 2;;
-
-#isl x;;
-true : bool
-
-#isl y;;
-false : bool
-\end{verbatim}
-}
-\SEEALSO
-inl, inr
-
-\ENDDOC
-\DOC{ISPEC}
-
-\TYPE {\small\verb%ISPEC : (term -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Specializes a theorem, with type instantiation if necessary.
-
-\DESCRIBE
-This rule specializes a quantified variable as does {\small\verb%SPEC%}; it differs
-from it in also instantiating the type if needed:
-{\par\samepage\setseps\small
-\begin{verbatim}
-     A |- !x:ty.tm
-  -----------------------  ISPEC "t:ty'"
-      A |- tm[t/x]
-\end{verbatim}
-}
-\noindent (where {\small\verb%t%} is free for {\small\verb%x%} in {\small\verb%tm%}, and {\small\verb%ty'%} is an instance
-of {\small\verb%ty%}).
-
-\FAILURE
-{\small\verb%ISPEC%} fails if the input theorem is not universally quantified, if
-the type of the given term is not an instance of the type of the
-quantified variable, or if the type variable is free in the
-assumptions.
-
-\SEEALSO
-INST_TY_TERM, INST_TYPE, ISPECL, SPEC, match.
-
-\ENDDOC
-\DOC{ISPECL}
-
-\TYPE {\small\verb%ISPECL : (term list -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Specializes a theorem zero or more times, with type instantiation if necessary.
+Maps a numeric term to the corresponding ML integer.
 
 \DESCRIBE
-{\small\verb%ISPECL%} is an iterative version of {\small\verb%ISPEC%}
+Given a term representing a natural number, i.e., of type {\small\verb%:num%}
+{\small\verb%int_of_term%} returns the corresponding ML integer constant.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-         A |- !x1...xn.t
-   ----------------------------  ISPECL ["t1",...,"tn"]
-    A |- t[t1,...tn/x1,...,xn]
+   #int_of_term "2";;
+   2 : int
 \end{verbatim}
 }
-\noindent (where {\small\verb%ti%} is free for {\small\verb%xi%} in {\small\verb%tm%}).
-
-\FAILURE
-{\small\verb%ISPECL%} fails if the list of terms is longer than the number of
-quantified variables in the term, if the type instantiation fails, or
-if the type variable being instantiated is free in the assumptions.
 
 \SEEALSO
-INST_TYPE, INST_TY_TERM, ISPEC, MATCH, SPEC, SPECL.
+term_of_int, string_of_int, int_of_string.
 
 \ENDDOC
 \DOC{is\_abs}
@@ -11896,24 +11814,6 @@
 mk_cons, dest_cons, mk_list, dest_list, is_list.
 
 \ENDDOC
-\DOC{is\_const}
-
-\TYPE {\small\verb%is_const : (term -> bool)%}\egroup
-
-\SYNOPSIS
-Tests a term to see if it is a constant.
-
-\DESCRIBE
-{\small\verb%is_const "const:ty"%} returns {\small\verb%true%}. If the term is not a constant the
-result is {\small\verb%false%}.
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-mk_const, dest_const, is_var, is_comb, is_abs.
-
-\ENDDOC
 \DOC{is\_constant}
 
 \TYPE {\small\verb%is_constant : (string -> bool)%}\egroup
@@ -11949,6 +11849,24 @@
 is_infix, is_binder
 
 \ENDDOC
+\DOC{is\_const}
+
+\TYPE {\small\verb%is_const : (term -> bool)%}\egroup
+
+\SYNOPSIS
+Tests a term to see if it is a constant.
+
+\DESCRIBE
+{\small\verb%is_const "const:ty"%} returns {\small\verb%true%}. If the term is not a constant the
+result is {\small\verb%false%}.
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+mk_const, dest_const, is_var, is_comb, is_abs.
+
+\ENDDOC
 \DOC{is\_definition}
 
 \TYPE {\small\verb%is_definition : (term -> bool)%}\egroup
@@ -12210,6 +12128,29 @@
 is_infix, is_type, is_binder_type
 
 \ENDDOC
+\DOC{isl}
+
+\TYPE {\small\verb%isl : ((* + **) -> bool)%}\egroup
+
+\SYNOPSIS
+Tests for membership of left summand.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#let x = inl 1 and y = inr 2;;
+
+#isl x;;
+true : bool
+
+#isl y;;
+false : bool
+\end{verbatim}
+}
+\SEEALSO
+inl, inr
+
+\ENDDOC
 \DOC{is\_let}
 
 \TYPE {\small\verb%is_let : (term -> bool)%}\egroup
@@ -12407,6 +12348,63 @@
 mk_pair, dest_pair.
 
 \ENDDOC
+\DOC{ISPEC}
+
+\TYPE {\small\verb%ISPEC : (term -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Specializes a theorem, with type instantiation if necessary.
+
+\DESCRIBE
+This rule specializes a quantified variable as does {\small\verb%SPEC%}; it differs
+from it in also instantiating the type if needed:
+{\par\samepage\setseps\small
+\begin{verbatim}
+     A |- !x:ty.tm
+  -----------------------  ISPEC "t:ty'"
+      A |- tm[t/x]
+\end{verbatim}
+}
+\noindent (where {\small\verb%t%} is free for {\small\verb%x%} in {\small\verb%tm%}, and {\small\verb%ty'%} is an instance
+of {\small\verb%ty%}).
+
+\FAILURE
+{\small\verb%ISPEC%} fails if the input theorem is not universally quantified, if
+the type of the given term is not an instance of the type of the
+quantified variable, or if the type variable is free in the
+assumptions.
+
+\SEEALSO
+INST_TY_TERM, INST_TYPE, ISPECL, SPEC, match.
+
+\ENDDOC
+\DOC{ISPECL}
+
+\TYPE {\small\verb%ISPECL : (term list -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Specializes a theorem zero or more times, with type instantiation if necessary.
+
+\DESCRIBE
+{\small\verb%ISPECL%} is an iterative version of {\small\verb%ISPEC%}
+{\par\samepage\setseps\small
+\begin{verbatim}
+         A |- !x1...xn.t
+   ----------------------------  ISPECL ["t1",...,"tn"]
+    A |- t[t1,...tn/x1,...,xn]
+\end{verbatim}
+}
+\noindent (where {\small\verb%ti%} is free for {\small\verb%xi%} in {\small\verb%tm%}).
+
+\FAILURE
+{\small\verb%ISPECL%} fails if the list of terms is longer than the number of
+quantified variables in the term, if the type instantiation fails, or
+if the type variable being instantiated is free in the assumptions.
+
+\SEEALSO
+INST_TYPE, INST_TY_TERM, ISPEC, MATCH, SPEC, SPECL.
+
+\ENDDOC
 \DOC{is\_pred}
 
 \TYPE {\small\verb%is_pred : (term -> bool)%}\egroup
@@ -12580,65 +12578,65 @@
 expression.
 
 \ENDDOC
-\DOC{itlist}
+\DOC{itlist2}
 
-\TYPE {\small\verb%itlist : ((* -> ** -> **) -> * list -> ** -> **)%}\egroup
+\TYPE {\small\verb%itlist2 : (((* # **) -> *** -> ***) -> (* list # ** list) -> *** -> ***)%}\egroup
 
 \SYNOPSIS
-List iteration function. Applies a binary function between adjacent elements
-of a list.
+Applies a paired function between adjacent elements of 2 lists.
 
 \DESCRIBE
-{\small\verb%itlist f [x1;...;xn] y%} returns
+{\small\verb%itlist2 f ([x1;...;xn],[y1;...;yn]) z%} returns
 {\par\samepage\setseps\small
 \begin{verbatim}
-   f x1 (f x2 ... (f xn y)...)
+   f (x1,y1) (f (x2,y2) ... (f (xn,yn) z)...)
 \end{verbatim}
 }
-\noindent It returns {\small\verb%y%} if list is empty.
+\noindent It returns {\small\verb%z%} if both lists are empty.
 
 \FAILURE
-Never fails.
+Fails with {\small\verb%itlist2%} if the two lists are of different lengths.
 
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#itlist (\x y. x + y) [1;2;3;4] 0;;
-10 : int
+#itlist2 (\(x,y) z. (x * y) + z) ([1;2],[3;4]) 0;;
+11 : int
 \end{verbatim}
 }
 \SEEALSO
-rev_itlist, end_itlist.
+itlist, rev_itlist, end_itlist, uncurry.
 
 \ENDDOC
-\DOC{itlist2}
+\DOC{itlist}
 
-\TYPE {\small\verb%itlist2 : (((* # **) -> *** -> ***) -> (* list # ** list) -> *** -> ***)%}\egroup
+\TYPE {\small\verb%itlist : ((* -> ** -> **) -> * list -> ** -> **)%}\egroup
 
 \SYNOPSIS
-Applies a paired function between adjacent elements of 2 lists.
+List iteration function. Applies a binary function between adjacent elements
+of a list.
 
 \DESCRIBE
-{\small\verb%itlist2 f ([x1;...;xn],[y1;...;yn]) z%} returns
+{\small\verb%itlist f [x1;...;xn] y%} returns
 {\par\samepage\setseps\small
 \begin{verbatim}
-   f (x1,y1) (f (x2,y2) ... (f (xn,yn) z)...)
+   f x1 (f x2 ... (f xn y)...)
 \end{verbatim}
 }
-\noindent It returns {\small\verb%z%} if both lists are empty.
+\noindent It returns {\small\verb%y%} if list is empty.
 
 \FAILURE
-Fails with {\small\verb%itlist2%} if the two lists are of different lengths.
+Never fails.
 
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#itlist2 (\(x,y) z. (x * y) + z) ([1;2],[3;4]) 0;;
-11 : int
+#itlist (\x y. x + y) [1;2;3;4] 0;;
+10 : int
 \end{verbatim}
 }
 \SEEALSO
-itlist, rev_itlist, end_itlist, uncurry.
+rev_itlist, end_itlist.
 
 \ENDDOC
 \DOC{K}
@@ -12672,6 +12670,34 @@
 \#, B, C, CB, Co, I, K, o, oo, S, W.
 
 \ENDDOC
+\DOC{LAST\_CONV}
+
+\TYPE {\small\verb%LAST_CONV : conv%}\egroup
+
+\SYNOPSIS
+Computes by inference the result of taking the last element of a list.
+
+\DESCRIBE
+For any object language list of the form {\small\verb%"[x0;...x(n-1)]"%} ,
+the result of evaluating
+{\par\samepage\setseps\small
+\begin{verbatim}
+   LAST_CONV "LAST [x0;...;x(n-1)]"
+\end{verbatim}
+}
+\noindent is the theorem
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- LAST [x0;...;x(n-1)] = x(n-1)
+\end{verbatim}
+}
+
+
+\FAILURE
+{\small\verb%LAST_CONV tm%} fails if {\small\verb%tm%} is an empty list.
+
+\ENDDOC
+
 \DOC{last}
 
 \TYPE {\small\verb%last : (* list -> *)%}\egroup
@@ -12718,34 +12744,6 @@
 
 \ENDDOC
 
-\DOC{LAST\_CONV}
-
-\TYPE {\small\verb%LAST_CONV : conv%}\egroup
-
-\SYNOPSIS
-Computes by inference the result of taking the last element of a list.
-
-\DESCRIBE
-For any object language list of the form {\small\verb%"[x0;...x(n-1)]"%} ,
-the result of evaluating
-{\par\samepage\setseps\small
-\begin{verbatim}
-   LAST_CONV "LAST [x0;...;x(n-1)]"
-\end{verbatim}
-}
-\noindent is the theorem
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- LAST [x0;...;x(n-1)] = x(n-1)
-\end{verbatim}
-}
-
-
-\FAILURE
-{\small\verb%LAST_CONV tm%} fails if {\small\verb%tm%} is an empty list.
-
-\ENDDOC
-
 \DOC{LEFT\_AND\_EXISTS\_CONV}
 
 \TYPE {\small\verb%LEFT_AND_EXISTS_CONV : conv%}\egroup
@@ -12902,17 +12900,6 @@
 OR_FORALL_CONV, FORALL_OR_CONV, RIGHT_OR_FORALL_CONV.
 
 \ENDDOC
-\DOC{length}
-
-\TYPE {\small\verb%length : (* list -> int)%}\egroup
-
-\SYNOPSIS
-Computes the length of a list: {\small\verb%length [x1;...;xn]%} returns {\small\verb%n%}.
-
-\FAILURE
-Never fails.
-
-\ENDDOC
 \DOC{LENGTH\_CONV}
 
 \TYPE {\small\verb%LENGTH_CONV : conv%}\egroup
@@ -12938,8 +12925,19 @@
 list.
 
 \FAILURE
-{\small\verb%LENGTH_CONV tm%} fails if {\small\verb%tm%} is not of the form {\small\verb%"LENGTH [x1;x2;...;xn]"%} or
-{\small\verb%"LENGTH []"%}.
+{\small\verb%LENGTH_CONV tm%} fails if {\small\verb%tm%} is not of the form {\small\verb%"LENGTH [x1;x2;...;xn]"%} or
+{\small\verb%"LENGTH []"%}.
+
+\ENDDOC
+\DOC{length}
+
+\TYPE {\small\verb%length : (* list -> int)%}\egroup
+
+\SYNOPSIS
+Computes the length of a list: {\small\verb%length [x1;...;xn]%} returns {\small\verb%n%}.
+
+\FAILURE
+Never fails.
 
 \ENDDOC
 \DOC{let\_after}
@@ -13418,6 +13416,25 @@
 system, unlink.
 
 \ENDDOC
+\DOC{lisp\_dir\_pathname}
+
+\TYPE {\small\verb%lisp_dir_pathname : string%}\egroup
+
+\SYNOPSIS
+Absolute pathname to the HOL lisp sources.
+
+\DESCRIBE
+For implementation reasons, the ML variable {\small\verb%lisp_dir_pathname%} is bound when
+the system if built to a string giving the absolute pathname of the directory
+containing the HOL lisp sources.  This value is not for general use.
+
+\FAILURE
+Evaluating {\small\verb%lisp_dir_pathname%} never fails.
+
+\SEEALSO
+ml_dir_pathname.
+
+\ENDDOC
 \DOC{lisp}
 
 \TYPE {\small\verb%lisp : (string -> void)%}\egroup
@@ -13464,25 +13481,6 @@
 dropout, lsp.
 
 \ENDDOC
-\DOC{lisp\_dir\_pathname}
-
-\TYPE {\small\verb%lisp_dir_pathname : string%}\egroup
-
-\SYNOPSIS
-Absolute pathname to the HOL lisp sources.
-
-\DESCRIBE
-For implementation reasons, the ML variable {\small\verb%lisp_dir_pathname%} is bound when
-the system if built to a string giving the absolute pathname of the directory
-containing the HOL lisp sources.  This value is not for general use.
-
-\FAILURE
-Evaluating {\small\verb%lisp_dir_pathname%} never fails.
-
-\SEEALSO
-ml_dir_pathname.
-
-\ENDDOC
 \DOC{LIST\_BETA\_CONV}
 
 \TYPE {\small\verb%LIST_BETA_CONV : conv%}\egroup
@@ -13855,6 +13853,28 @@
 disjuncts, mk_disj.
 
 \ENDDOC
+\DOC{list\_mk\_exists}
+
+\TYPE {\small\verb%list_mk_exists : ((term list # term) -> term)%}\egroup
+
+\SYNOPSIS
+Iteratively constructs existential quantifications.
+
+\DESCRIBE
+{\small\verb%list_mk_exists(["x1";...;"xn"],"t")%} returns {\small\verb%"?x1 ... xn. t"%}.
+
+\FAILURE
+Fails with {\small\verb%list_mk_exists%} if the terms in the list are not variables or if
+{\small\verb%t%} is not of type {\small\verb%":bool"%} and the list of terms is non-empty. If the list
+of terms is empty the type of {\small\verb%t%} can be anything.
+
+\COMMENTS
+The system shows the type as {\small\verb%(goal -> term)%}.
+
+\SEEALSO
+strip_exists, mk_exists.
+
+\ENDDOC
 \DOC{LIST\_MK\_EXISTS}
 
 \TYPE {\small\verb%LIST_MK_EXISTS : (term list -> thm -> thm)%}\egroup
@@ -13884,28 +13904,6 @@
 EXISTS_EQ, MK_EXISTS.
 
 \ENDDOC
-\DOC{list\_mk\_exists}
-
-\TYPE {\small\verb%list_mk_exists : ((term list # term) -> term)%}\egroup
-
-\SYNOPSIS
-Iteratively constructs existential quantifications.
-
-\DESCRIBE
-{\small\verb%list_mk_exists(["x1";...;"xn"],"t")%} returns {\small\verb%"?x1 ... xn. t"%}.
-
-\FAILURE
-Fails with {\small\verb%list_mk_exists%} if the terms in the list are not variables or if
-{\small\verb%t%} is not of type {\small\verb%":bool"%} and the list of terms is non-empty. If the list
-of terms is empty the type of {\small\verb%t%} can be anything.
-
-\COMMENTS
-The system shows the type as {\small\verb%(goal -> term)%}.
-
-\SEEALSO
-strip_exists, mk_exists.
-
-\ENDDOC
 \DOC{list\_mk\_forall}
 
 \TYPE {\small\verb%list_mk_forall : ((term list # term) -> term)%}\egroup
@@ -14035,115 +14033,6 @@
 Evaluating the assignable variable {\small\verb%list_of_binders%} never fails.
 
 \ENDDOC
-\DOC{load}
-
-\TYPE {\small\verb%load : ((string # bool) -> void)%}\egroup
-
-\SYNOPSIS
-Loads ML phrases from the named file.
-
-\DESCRIBE
-A call {\small\verb%load(`file`,flag)%} will load ML phrases from the file described by
-{\small\verb%file%}. If the boolean value {\small\verb%flag%} is true, then toplevel printing of the
-system responses will occur, otherwise just a dot is printed for each toplevel
-phrase. The name {\small\verb%file%} is expanded into a real filename using the same
-mechanism as {\small\verb%find_ml_file%}.
-
-\FAILURE
-Fails if the appropriate file cannot be found on the search path, or if an
-error occurs in the ML which is being loaded.
-
-\COMMENTS
-It is usual to use either {\small\verb%loadf%} or {\small\verb%loadt%} rather than this function, which
-perform the same action with one or the other setting of the flag.
-
-\SEEALSO
-find_ml_file, loadf, loadt, search_path, set_search_path.
-
-\ENDDOC
-\DOC{loadf}
-
-\TYPE {\small\verb%loadf : (string -> void)%}\egroup
-
-\SYNOPSIS
-Loads an ML file with the verbose flag set to {\small\verb%false%}.
-
-\DESCRIBE
-The function {\small\verb%loadf%} takes a string indicating the ML file name as
-argument and loads it in the same manner as {\small\verb%load%}, except that the
-verbose flag is always set to false.
-
-\FAILURE
-{\small\verb%loadf%} will fail if the file named by the argument does not exist in
-the search path. It will fail in the same manner if the file is not a
-valid  ML file. Failure in the ML file will terminate loading.
-
-\EXAMPLE
-If we have a ML file called {\small\verb%foo.ml%} which contains the line
-{\par\samepage\setseps\small
-\begin{verbatim}
-   let x=2+2;;
-\end{verbatim}
-}
-\noindent this can be loaded as follows:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #loadf `foo.ml`;;
-\end{verbatim}
-}
-\noindent and the system would respond with:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   .() : void
-\end{verbatim}
-}
-\SEEALSO
-load, loadf.
-
-\ENDDOC
-\DOC{loadt}
-
-\TYPE {\small\verb%loadt : (string -> void)%}\egroup
-
-\SYNOPSIS
-{\small\verb%loadt%} loads an ML file with the verbose flag set to {\small\verb%true%}.
-
-\DESCRIBE
-The function {\small\verb%loadt%} takes a string indicating the ML file name as
-argument and loads it in the same manner as {\small\verb%load%}, except that the
-verbose flag is always set to {\small\verb%true%}.
-
-\FAILURE
-{\small\verb%loadt%} will fail if the file named by the argument does not exist in
-the search path. It will fail in the same manner if the file is not a
-valid ML file. Failure in the ML file will also terminate loading.
-
-\EXAMPLE
-If we have an ML file called {\small\verb%foo.ml%} which contains the line
-{\par\samepage\setseps\small
-\begin{verbatim}
-   let x=2+2;;
-\end{verbatim}
-}
-\noindent this can be loaded as follows:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #loadt `foo.ml`;;
-\end{verbatim}
-}
-\noindent and the system would respond with:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   x = 4 : int
-
-   File foo.ml loaded
-   () : void
-\end{verbatim}
-}
-\SEEALSO
-load, loadf.
-
-\ENDDOC
 \DOC{load\_axiom}
 
 \TYPE {\small\verb%load_axiom : (string -> string -> void)%}\egroup
@@ -14320,7 +14209,73 @@
 \end{verbatim}
 }
 \SEEALSO
-definitions, let_after, let_before, load_definition.
+definitions, let_after, let_before, load_definition.
+
+\ENDDOC
+\DOC{load}
+
+\TYPE {\small\verb%load : ((string # bool) -> void)%}\egroup
+
+\SYNOPSIS
+Loads ML phrases from the named file.
+
+\DESCRIBE
+A call {\small\verb%load(`file`,flag)%} will load ML phrases from the file described by
+{\small\verb%file%}. If the boolean value {\small\verb%flag%} is true, then toplevel printing of the
+system responses will occur, otherwise just a dot is printed for each toplevel
+phrase. The name {\small\verb%file%} is expanded into a real filename using the same
+mechanism as {\small\verb%find_ml_file%}.
+
+\FAILURE
+Fails if the appropriate file cannot be found on the search path, or if an
+error occurs in the ML which is being loaded.
+
+\COMMENTS
+It is usual to use either {\small\verb%loadf%} or {\small\verb%loadt%} rather than this function, which
+perform the same action with one or the other setting of the flag.
+
+\SEEALSO
+find_ml_file, loadf, loadt, search_path, set_search_path.
+
+\ENDDOC
+\DOC{loadf}
+
+\TYPE {\small\verb%loadf : (string -> void)%}\egroup
+
+\SYNOPSIS
+Loads an ML file with the verbose flag set to {\small\verb%false%}.
+
+\DESCRIBE
+The function {\small\verb%loadf%} takes a string indicating the ML file name as
+argument and loads it in the same manner as {\small\verb%load%}, except that the
+verbose flag is always set to false.
+
+\FAILURE
+{\small\verb%loadf%} will fail if the file named by the argument does not exist in
+the search path. It will fail in the same manner if the file is not a
+valid  ML file. Failure in the ML file will terminate loading.
+
+\EXAMPLE
+If we have a ML file called {\small\verb%foo.ml%} which contains the line
+{\par\samepage\setseps\small
+\begin{verbatim}
+   let x=2+2;;
+\end{verbatim}
+}
+\noindent this can be loaded as follows:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #loadf `foo.ml`;;
+\end{verbatim}
+}
+\noindent and the system would respond with:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   .() : void
+\end{verbatim}
+}
+\SEEALSO
+load, loadf.
 
 \ENDDOC
 \DOC{load\_library}
@@ -14395,6 +14350,49 @@
 libraries, library_pathname, library_search_path, set_library_search_path.
 
 \ENDDOC
+\DOC{loadt}
+
+\TYPE {\small\verb%loadt : (string -> void)%}\egroup
+
+\SYNOPSIS
+{\small\verb%loadt%} loads an ML file with the verbose flag set to {\small\verb%true%}.
+
+\DESCRIBE
+The function {\small\verb%loadt%} takes a string indicating the ML file name as
+argument and loads it in the same manner as {\small\verb%load%}, except that the
+verbose flag is always set to {\small\verb%true%}.
+
+\FAILURE
+{\small\verb%loadt%} will fail if the file named by the argument does not exist in
+the search path. It will fail in the same manner if the file is not a
+valid ML file. Failure in the ML file will also terminate loading.
+
+\EXAMPLE
+If we have an ML file called {\small\verb%foo.ml%} which contains the line
+{\par\samepage\setseps\small
+\begin{verbatim}
+   let x=2+2;;
+\end{verbatim}
+}
+\noindent this can be loaded as follows:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #loadt `foo.ml`;;
+\end{verbatim}
+}
+\noindent and the system would respond with:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   x = 4 : int
+
+   File foo.ml loaded
+   () : void
+\end{verbatim}
+}
+\SEEALSO
+load, loadf.
+
+\ENDDOC
 \DOC{load\_theorem}
 
 \TYPE {\small\verb%load_theorem : (string -> string -> void)%}\egroup
@@ -14584,54 +14582,6 @@
 dropout, lisp.
 
 \ENDDOC
-\DOC{map}
-
-\TYPE {\small\verb%map : ((* -> **) -> * list -> ** list)%}\egroup
-
-\SYNOPSIS
-Applies a function to every element of a list.
-
-\DESCRIBE
-{\small\verb%map f [x1;...;xn]%} returns {\small\verb%[(f x1);...;(f xn)]%}.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#map (\x. x * 2) [];;
-[] : int list
-
-#map (\x. x * 2) [1;2;3];;
-[2; 4; 6] : int list
-\end{verbatim}
-}
-\ENDDOC
-\DOC{map2}
-
-\TYPE {\small\verb%map2 : (((* # **) -> ***) -> (* list # ** list) -> *** list)%}\egroup
-
-\SYNOPSIS
-Maps a binary function over two lists to create one new list.
-
-\DESCRIBE
-{\small\verb%map2 f ([x1;...;xn],[y1;...;yn])%} returns {\small\verb%[f(x1,y1);...;f(xn,yn)]%}.
-
-\FAILURE
-Fails with {\small\verb%map2%} if the two lists are of different lengths.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#map2 $+ ([1;2;3],[3;2;1]);;
-[4; 4; 4] : int list
-\end{verbatim}
-}
-\SEEALSO
-map, uncurry.
-
-\ENDDOC
 \DOC{MAP2\_CONV}
 
 \TYPE {\small\verb%MAP2_CONV : conv -> conv%}\egroup
@@ -14685,62 +14635,28 @@
 
 \ENDDOC
 
-\DOC{mapfilter}
-
-\TYPE {\small\verb%mapfilter : ((* -> **) -> * list -> ** list)%}\egroup
-
-\SYNOPSIS
-Applies a function to every element of a list, returning a list of results
-for those elements for which application succeeds.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#mapfilter hd [[1;2;3];[4;5];[];[6;7;8];[]];;
-[1; 4; 6] : int list
-\end{verbatim}
-}
-\SEEALSO
-filter, map.
-
-\ENDDOC
-\DOC{maptok}
+\DOC{map2}
 
-\TYPE {\small\verb%maptok : ((string -> *) -> string -> * list)%}\egroup
+\TYPE {\small\verb%map2 : (((* # **) -> ***) -> (* list # ** list) -> *** list)%}\egroup
 
 \SYNOPSIS
-Maps a function over the constituent words of a string.
+Maps a binary function over two lists to create one new list.
 
 \DESCRIBE
-{\small\verb%maptok f s%} first splits the string {\small\verb%s%} into a list of substrings, and then
-maps the function {\small\verb%f%} over that list. Splitting of the string occurs at each
-sequence of blanks and carriage returns (white space). This white space does
-not appear in the list of substrings. Leading and trailing white space in the
-input string is also thrown away.
+{\small\verb%map2 f ([x1;...;xn],[y1;...;yn])%} returns {\small\verb%[f(x1,y1);...;f(xn,yn)]%}.
 
 \FAILURE
-Fails if one of the applications of {\small\verb%f%} to a substring fails.
+Fails with {\small\verb%map2%} if the two lists are of different lengths.
 
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#maptok explode `  the cat  sat `;;
-[[`t`; `h`; `e`]; [`c`; `a`; `t`]; [`s`; `a`; `t`]] : string list list
-\end{verbatim}
-}
-\USES
-Useful when wanting to map a function over a list of constant strings.
-Instead of using {\small\verb%map f [`string1`;...;`stringn`]%} one can use:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   (maptok f `string1 ... stringn`)
+#map2 $+ ([1;2;3],[3;2;1]);;
+[4; 4; 4] : int list
 \end{verbatim}
 }
 \SEEALSO
-words, word_separators, words2, map.
+map, uncurry.
 
 \ENDDOC
 \DOC{MAP\_CONV}
@@ -14819,6 +14735,30 @@
 
 \ENDDOC
 
+\DOC{map}
+
+\TYPE {\small\verb%map : ((* -> **) -> * list -> ** list)%}\egroup
+
+\SYNOPSIS
+Applies a function to every element of a list.
+
+\DESCRIBE
+{\small\verb%map f [x1;...;xn]%} returns {\small\verb%[(f x1);...;(f xn)]%}.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#map (\x. x * 2) [];;
+[] : int list
+
+#map (\x. x * 2) [1;2;3];;
+[2; 4; 6] : int list
+\end{verbatim}
+}
+\ENDDOC
 \DOC{MAP\_EVERY}
 
 \TYPE {\small\verb%MAP_EVERY : ((* -> tactic) -> * list -> tactic)%}\egroup
@@ -14848,41 +14788,148 @@
 A convenient way of doing case analysis over several boolean variables is:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   MAP_EVERY BOOL_CASES_TAC ["var1:bool";...;"varn:bool"]
+   MAP_EVERY BOOL_CASES_TAC ["var1:bool";...;"varn:bool"]
+\end{verbatim}
+}
+\SEEALSO
+EVERY, FIRST, MAP_FIRST, THEN.
+
+\ENDDOC
+\DOC{mapfilter}
+
+\TYPE {\small\verb%mapfilter : ((* -> **) -> * list -> ** list)%}\egroup
+
+\SYNOPSIS
+Applies a function to every element of a list, returning a list of results
+for those elements for which application succeeds.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#mapfilter hd [[1;2;3];[4;5];[];[6;7;8];[]];;
+[1; 4; 6] : int list
+\end{verbatim}
+}
+\SEEALSO
+filter, map.
+
+\ENDDOC
+\DOC{MAP\_FIRST}
+
+\TYPE {\small\verb%MAP_FIRST : ((* -> tactic) -> * list -> tactic)%}\egroup
+
+\SYNOPSIS
+Applies first tactic that succeeds in a list given by mapping a function over a
+list.
+
+\DESCRIBE
+When applied to a tactic-producing function {\small\verb%f%} and an operand list
+{\small\verb%[x1;...;xn]%}, the elements of which have the same type as {\small\verb%f%}'s domain
+type, {\small\verb%MAP_FIRST%} maps the function {\small\verb%f%} over the list, producing a list of
+tactics, then tries applying these tactics to the goal till one succeeds.
+If {\small\verb%f(xm)%} is the first to succeed, then the overall effect is the same
+as applying {\small\verb%f(xm)%}. Thus:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   MAP_FIRST f [x1;...;xn] = (f x1) ORELSE ... ORELSE (f xn)
+\end{verbatim}
+}
+\FAILURE
+The application of {\small\verb%MAP_FIRST%} to a function and tactic list fails iff
+the function does when applied to any of the elements of the list. The
+resulting tactic fails iff all the resulting tactics fail when
+applied to the goal.
+
+\SEEALSO
+EVERY, FIRST, MAP_EVERY, ORELSE.
+
+\ENDDOC
+\DOC{maptok}
+
+\TYPE {\small\verb%maptok : ((string -> *) -> string -> * list)%}\egroup
+
+\SYNOPSIS
+Maps a function over the constituent words of a string.
+
+\DESCRIBE
+{\small\verb%maptok f s%} first splits the string {\small\verb%s%} into a list of substrings, and then
+maps the function {\small\verb%f%} over that list. Splitting of the string occurs at each
+sequence of blanks and carriage returns (white space). This white space does
+not appear in the list of substrings. Leading and trailing white space in the
+input string is also thrown away.
+
+\FAILURE
+Fails if one of the applications of {\small\verb%f%} to a substring fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#maptok explode `  the cat  sat `;;
+[[`t`; `h`; `e`]; [`c`; `a`; `t`]; [`s`; `a`; `t`]] : string list list
+\end{verbatim}
+}
+\USES
+Useful when wanting to map a function over a list of constant strings.
+Instead of using {\small\verb%map f [`string1`;...;`stringn`]%} one can use:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   (maptok f `string1 ... stringn`)
 \end{verbatim}
 }
 \SEEALSO
-EVERY, FIRST, MAP_FIRST, THEN.
+words, word_separators, words2, map.
 
 \ENDDOC
-\DOC{MAP\_FIRST}
+\DOC{MATCH\_ACCEPT\_TAC}
 
-\TYPE {\small\verb%MAP_FIRST : ((* -> tactic) -> * list -> tactic)%}\egroup
+\TYPE {\small\verb%MATCH_ACCEPT_TAC : thm_tactic%}\egroup
 
 \SYNOPSIS
-Applies first tactic that succeeds in a list given by mapping a function over a
-list.
+Solves a goal which is an instance of the supplied theorem.
 
 \DESCRIBE
-When applied to a tactic-producing function {\small\verb%f%} and an operand list
-{\small\verb%[x1;...;xn]%}, the elements of which have the same type as {\small\verb%f%}'s domain
-type, {\small\verb%MAP_FIRST%} maps the function {\small\verb%f%} over the list, producing a list of
-tactics, then tries applying these tactics to the goal till one succeeds.
-If {\small\verb%f(xm)%} is the first to succeed, then the overall effect is the same
-as applying {\small\verb%f(xm)%}. Thus:
+When given a theorem {\small\verb%A' |- t%} and a goal {\small\verb%A ?- t'%} where {\small\verb%t%} can be matched
+to {\small\verb%t'%} by instantiating variables which are either free or
+universally quantified at the outer level, including appropriate type
+instantiation, {\small\verb%MATCH_ACCEPT_TAC%} completely solves the goal.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   MAP_FIRST f [x1;...;xn] = (f x1) ORELSE ... ORELSE (f xn)
+    A ?- t'
+   =========  MATCH_ACCEPT_TAC (A' |- t)
+
 \end{verbatim}
 }
+\noindent Unless {\small\verb%A'%} is a subset of {\small\verb%A%}, this is an invalid tactic.
+
 \FAILURE
-The application of {\small\verb%MAP_FIRST%} to a function and tactic list fails iff
-the function does when applied to any of the elements of the list. The
-resulting tactic fails iff all the resulting tactics fail when
-applied to the goal.
+Fails unless the theorem has a conclusion which is instantiable to match that
+of the goal.
 
+\EXAMPLE
+The following example shows variable and type instantiation at work. We can use
+the polymorphic list theorem {\small\verb%HD%}:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   HD = |- !h t. HD(CONS h t) = h
+\end{verbatim}
+}
+\noindent to solve the goal:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   ?- HD [1;2] = 1
+\end{verbatim}
+}
+\noindent simply by:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   MATCH_ACCEPT_TAC HD
+\end{verbatim}
+}
 \SEEALSO
-EVERY, FIRST, MAP_EVERY, ORELSE.
+ACCEPT_TAC.
 
 \ENDDOC
 \DOC{match}
@@ -14946,55 +14993,6 @@
 INST_TY_TERM, PART_MATCH.
 
 \ENDDOC
-\DOC{MATCH\_ACCEPT\_TAC}
-
-\TYPE {\small\verb%MATCH_ACCEPT_TAC : thm_tactic%}\egroup
-
-\SYNOPSIS
-Solves a goal which is an instance of the supplied theorem.
-
-\DESCRIBE
-When given a theorem {\small\verb%A' |- t%} and a goal {\small\verb%A ?- t'%} where {\small\verb%t%} can be matched
-to {\small\verb%t'%} by instantiating variables which are either free or
-universally quantified at the outer level, including appropriate type
-instantiation, {\small\verb%MATCH_ACCEPT_TAC%} completely solves the goal.
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A ?- t'
-   =========  MATCH_ACCEPT_TAC (A' |- t)
-
-\end{verbatim}
-}
-\noindent Unless {\small\verb%A'%} is a subset of {\small\verb%A%}, this is an invalid tactic.
-
-\FAILURE
-Fails unless the theorem has a conclusion which is instantiable to match that
-of the goal.
-
-\EXAMPLE
-The following example shows variable and type instantiation at work. We can use
-the polymorphic list theorem {\small\verb%HD%}:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   HD = |- !h t. HD(CONS h t) = h
-\end{verbatim}
-}
-\noindent to solve the goal:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ?- HD [1;2] = 1
-\end{verbatim}
-}
-\noindent simply by:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   MATCH_ACCEPT_TAC HD
-\end{verbatim}
-}
-\SEEALSO
-ACCEPT_TAC.
-
-\ENDDOC
 \DOC{MATCH\_MP}
 
 \TYPE {\small\verb%MATCH_MP : (thm -> thm -> thm)%}\egroup
@@ -15188,6 +15186,23 @@
 print_string, print_tok, print_begin, print_end, print_newline.
 
 \ENDDOC
+\DOC{mk\_abs}
+
+\TYPE {\small\verb%mk_abs : ((term # term) -> term)%}\egroup
+
+\SYNOPSIS
+Constructs an abstraction.
+
+\DESCRIBE
+{\small\verb%mk_abs "var","t"%} returns the abstraction {\small\verb%"\var. t"%}.
+
+\FAILURE
+Fails with {\small\verb%mk_abs%} if first term is not a variable.
+
+\SEEALSO
+dest_abs, is_abs, list_mk_abs, mk_var, mk_const, mk_comb.
+
+\ENDDOC
 \DOC{MK\_ABS}
 
 \TYPE {\small\verb%MK_ABS : (thm -> thm)%}\egroup
@@ -15213,21 +15228,31 @@
 ABS, HALF_MK_ABS, MK_COMB, MK_EXISTS.
 
 \ENDDOC
-\DOC{mk\_abs}
+\DOC{mk\_comb}
 
-\TYPE {\small\verb%mk_abs : ((term # term) -> term)%}\egroup
+\TYPE {\small\verb%mk_comb : ((term # term) -> term)%}\egroup
 
 \SYNOPSIS
-Constructs an abstraction.
+Constructs a combination (function application).
 
 \DESCRIBE
-{\small\verb%mk_abs "var","t"%} returns the abstraction {\small\verb%"\var. t"%}.
+{\small\verb%mk_comb "t1","t2"%} returns the combination {\small\verb%"t1 t2"%}.
 
 \FAILURE
-Fails with {\small\verb%mk_abs%} if first term is not a variable.
+Fails with {\small\verb%mk_comb%} unless {\small\verb%t1%} is a function with domain type {\small\verb%t2%}.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#mk_comb("$~","T");;
+"~T" : term
 
+#mk_comb("T","T");;
+evaluation failed     mk_comb
+\end{verbatim}
+}
 \SEEALSO
-dest_abs, is_abs, list_mk_abs, mk_var, mk_const, mk_comb.
+dest_comb, is_comb, list_mk_comb, mk_var, mk_const, mk_abs.
 
 \ENDDOC
 \DOC{MK\_COMB}
@@ -15257,33 +15282,6 @@
 AP_TERM, AP_THM.
 
 \ENDDOC
-\DOC{mk\_comb}
-
-\TYPE {\small\verb%mk_comb : ((term # term) -> term)%}\egroup
-
-\SYNOPSIS
-Constructs a combination (function application).
-
-\DESCRIBE
-{\small\verb%mk_comb "t1","t2"%} returns the combination {\small\verb%"t1 t2"%}.
-
-\FAILURE
-Fails with {\small\verb%mk_comb%} unless {\small\verb%t1%} is a function with domain type {\small\verb%t2%}.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#mk_comb("$~","T");;
-"~T" : term
-
-#mk_comb("T","T");;
-evaluation failed     mk_comb
-\end{verbatim}
-}
-\SEEALSO
-dest_comb, is_comb, list_mk_comb, mk_var, mk_const, mk_abs.
-
-\ENDDOC
 \DOC{mk\_cond}
 
 \TYPE {\small\verb%mk_cond : ((term # term # term) -> term)%}\egroup
@@ -15421,6 +15419,24 @@
 dest_eq, is_eq.
 
 \ENDDOC
+\DOC{mk\_exists}
+
+\TYPE {\small\verb%mk_exists : ((term # term) -> term)%}\egroup
+
+\SYNOPSIS
+Constructs an existential quantification.
+
+\DESCRIBE
+{\small\verb%mk_exists("var","t")%} returns {\small\verb%"?var. t"%}.
+
+\FAILURE
+Fails with {\small\verb%mk_exists%} if first term is not a variable or if {\small\verb%t%} is not of
+type {\small\verb%":bool"%}.
+
+\SEEALSO
+dest_exists, is_exists, list_mk_exists.
+
+\ENDDOC
 \DOC{MK\_EXISTS}
 
 \TYPE {\small\verb%MK_EXISTS : (thm -> thm)%}\egroup
@@ -15446,24 +15462,6 @@
 AP_TERM, EXISTS_EQ, GEN, LIST_MK_EXISTS, MK_ABS.
 
 \ENDDOC
-\DOC{mk\_exists}
-
-\TYPE {\small\verb%mk_exists : ((term # term) -> term)%}\egroup
-
-\SYNOPSIS
-Constructs an existential quantification.
-
-\DESCRIBE
-{\small\verb%mk_exists("var","t")%} returns {\small\verb%"?var. t"%}.
-
-\FAILURE
-Fails with {\small\verb%mk_exists%} if first term is not a variable or if {\small\verb%t%} is not of
-type {\small\verb%":bool"%}.
-
-\SEEALSO
-dest_exists, is_exists, list_mk_exists.
-
-\ENDDOC
 \DOC{mk\_forall}
 
 \TYPE {\small\verb%mk_forall : ((term # term) -> term)%}\egroup
@@ -16111,58 +16109,23 @@
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#new_theory `gurk`;;
-() : void
-
-#new_axiom(`untrue`,"x = 1");;
-|- !x. x = 1
-\end{verbatim}
-}
-\COMMENTS
-For most purposes, it is unnecessary to declare new axioms: all of classical
-mathematics can be derived by definitional extension alone. Proceeding by
-definition is not only more elegant, but also guarantees the consistency of the
-deductions made. However, there are certain entities which cannot be modelled
-in simple type theory without further axioms, such as higher transfinite
-ordinals.
-
-\SEEALSO
-mk_thm, new_definition.
-
-\ENDDOC
-\DOC{new\_binder}
-
-\TYPE {\small\verb%new_binder : ((string # type) -> void)%}\egroup
-
-\SYNOPSIS
-Sets up a new binder in the current theory.
-
-\DESCRIBE
-A call {\small\verb%new_binder(`bnd`,":ty")%} declares a new binder {\small\verb%bnd%} in the current
-theory. The type must be of the form {\small\verb%(* -> **) -> ***%}, because being a binder,
-{\small\verb%bnd%} will apply to an abstraction; for example {\small\verb%"!x:bool. (x=T) \/ (x=F)"%} is
-actually a prettyprinting of {\small\verb%"$! (\x. (x=T) \/ (x=F))"%}.
-
-\FAILURE
-Fails if HOL is not in draft mode, or there is already a constant of some sort
-of that name in the current theory, or if the type does not correspond to the
-above pattern.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#new_theory `anorak`;;
-() : void
-
-#new_binder(`!!`,":(bool->bool)->bool");;
+#new_theory `gurk`;;
 () : void
 
-#"!!x. T";;
-"!! x. T" : term
+#new_axiom(`untrue`,"x = 1");;
+|- !x. x = 1
 \end{verbatim}
 }
+\COMMENTS
+For most purposes, it is unnecessary to declare new axioms: all of classical
+mathematics can be derived by definitional extension alone. Proceeding by
+definition is not only more elegant, but also guarantees the consistency of the
+deductions made. However, there are certain entities which cannot be modelled
+in simple type theory without further axioms, such as higher transfinite
+ordinals.
+
 \SEEALSO
-binders, is_binder.
+mk_thm, new_definition.
 
 \ENDDOC
 \DOC{new\_binder\_definition}
@@ -16244,6 +16207,41 @@
 new_list_rec_definition, new_prim_rec_definition.
 
 \ENDDOC
+\DOC{new\_binder}
+
+\TYPE {\small\verb%new_binder : ((string # type) -> void)%}\egroup
+
+\SYNOPSIS
+Sets up a new binder in the current theory.
+
+\DESCRIBE
+A call {\small\verb%new_binder(`bnd`,":ty")%} declares a new binder {\small\verb%bnd%} in the current
+theory. The type must be of the form {\small\verb%(* -> **) -> ***%}, because being a binder,
+{\small\verb%bnd%} will apply to an abstraction; for example {\small\verb%"!x:bool. (x=T) \/ (x=F)"%} is
+actually a prettyprinting of {\small\verb%"$! (\x. (x=T) \/ (x=F))"%}.
+
+\FAILURE
+Fails if HOL is not in draft mode, or there is already a constant of some sort
+of that name in the current theory, or if the type does not correspond to the
+above pattern.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#new_theory `anorak`;;
+() : void
+
+#new_binder(`!!`,":(bool->bool)->bool");;
+() : void
+
+#"!!x. T";;
+"!! x. T" : term
+\end{verbatim}
+}
+\SEEALSO
+binders, is_binder.
+
+\ENDDOC
 \DOC{new\_constant}
 
 \TYPE {\small\verb%new_constant : ((string # type) -> void)%}\egroup
@@ -16415,46 +16413,6 @@
 new_specification.
 
 \ENDDOC
-\DOC{new\_infix}
-
-\TYPE {\small\verb%new_infix : ((string # type) -> void)%}\egroup
-
-\SYNOPSIS
-Declares a new infix constant in the current theory.
-
-\DESCRIBE
-A call {\small\verb%new_infix(`i`,":ty")%} makes {\small\verb%i%} an infix
-constant in the current theory. Note that it does not specifiy its value.
-The constant may have a polymorphic type, which may be arbitrarily
-instantiated. Like any other infix or binder, its special parse status may be
-suppressed by preceding it with a dollar sign.
-
-\FAILURE
-Fails if HOL is not in draft mode, or if the name is not a valid constant
-name, or there is already a constant of that name in the current theory.
-
-\EXAMPLE
-The following shows the use of the curried form as well as the infix:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #new_theory `groke`;;
-   () : void
-
-   #new_infix(`orelse`,":bool->bool->bool");;
-   () : void
-
-   #"T orelse F";;
-   "T orelse F" : term
-
-   #"$orelse T F";;
-   "T orelse F" : term
-\end{verbatim}
-}
-\SEEALSO
-constants, infixes, is_constant, is_infix, new_constant, new_definition,
-new_infix_definition.
-
-\ENDDOC
 \DOC{new\_infix\_definition}
 
 \TYPE {\small\verb%new_infix_definition : ((string # term) -> thm)%}\egroup
@@ -16530,6 +16488,46 @@
 new_prim_rec_definition.
 
 \ENDDOC
+\DOC{new\_infix}
+
+\TYPE {\small\verb%new_infix : ((string # type) -> void)%}\egroup
+
+\SYNOPSIS
+Declares a new infix constant in the current theory.
+
+\DESCRIBE
+A call {\small\verb%new_infix(`i`,":ty")%} makes {\small\verb%i%} an infix
+constant in the current theory. Note that it does not specifiy its value.
+The constant may have a polymorphic type, which may be arbitrarily
+instantiated. Like any other infix or binder, its special parse status may be
+suppressed by preceding it with a dollar sign.
+
+\FAILURE
+Fails if HOL is not in draft mode, or if the name is not a valid constant
+name, or there is already a constant of that name in the current theory.
+
+\EXAMPLE
+The following shows the use of the curried form as well as the infix:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #new_theory `groke`;;
+   () : void
+
+   #new_infix(`orelse`,":bool->bool->bool");;
+   () : void
+
+   #"T orelse F";;
+   "T orelse F" : term
+
+   #"$orelse T F";;
+   "T orelse F" : term
+\end{verbatim}
+}
+\SEEALSO
+constants, infixes, is_constant, is_infix, new_constant, new_definition,
+new_infix_definition.
+
+\ENDDOC
 \DOC{new\_infix\_list\_rec\_definition}
 
 \TYPE {\small\verb%new_infix_list_rec_definition : ((string # term) -> thm)%}\egroup
@@ -17401,43 +17399,6 @@
 new_specification, new_type, print_theory, save_thm, search_path.
 
 \ENDDOC
-\DOC{new\_type}
-
-\TYPE {\small\verb%new_type : (int -> string -> void)%}\egroup
-
-\SYNOPSIS
-Declares a new type or type constructor.
-
-\DESCRIBE
-A call {\small\verb%new_type n `t`%} declares a new {\small\verb%n%}-ary type constructor called {\small\verb%t%} in
-the current theory segment. If {\small\verb%n%} is zero, this is just a new base type.
-
-\FAILURE
-Fails if HOL is not in draft mode, or if the name is not a valid type
-name, or there is already a type operator of that name in the current theory.
-
-\EXAMPLE
-A version of ZF set theory might declare a new type {\small\verb%set%} and start using it as
-follows:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #new_theory `ZF`;;
-   () : void
-
-   #new_type 0 `set`;;
-   () : void
-
-   #new_infix(`mem`,":set->set->bool");;
-   () : void
-
-   #new_axiom(`ext`,"(!z. z mem x = z mem y) ==> (x = y)");;
-   |- !x y. (!z. z mem x = z mem y) ==> (x = y)
-\end{verbatim}
-}
-\SEEALSO
-types, type_abbrevs, new_type_abbrev.
-
-\ENDDOC
 \DOC{new\_type\_abbrev}
 
 \TYPE {\small\verb%new_type_abbrev : ((string # type) -> void)%}\egroup
@@ -17545,6 +17506,43 @@
 prove_rep_fn_one_one, prove_rep_fn_onto.
 
 \ENDDOC
+\DOC{new\_type}
+
+\TYPE {\small\verb%new_type : (int -> string -> void)%}\egroup
+
+\SYNOPSIS
+Declares a new type or type constructor.
+
+\DESCRIBE
+A call {\small\verb%new_type n `t`%} declares a new {\small\verb%n%}-ary type constructor called {\small\verb%t%} in
+the current theory segment. If {\small\verb%n%} is zero, this is just a new base type.
+
+\FAILURE
+Fails if HOL is not in draft mode, or if the name is not a valid type
+name, or there is already a type operator of that name in the current theory.
+
+\EXAMPLE
+A version of ZF set theory might declare a new type {\small\verb%set%} and start using it as
+follows:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #new_theory `ZF`;;
+   () : void
+
+   #new_type 0 `set`;;
+   () : void
+
+   #new_infix(`mem`,":set->set->bool");;
+   () : void
+
+   #new_axiom(`ext`,"(!z. z mem x = z mem y) ==> (x = y)");;
+   |- !x y. (!z. z mem x = z mem y) ==> (x = y)
+\end{verbatim}
+}
+\SEEALSO
+types, type_abbrevs, new_type_abbrev.
+
+\ENDDOC
 \DOC{nil\_term\_net}
 
 \TYPE {\small\verb%nil_term_net : * term_net%}\egroup
@@ -17554,6 +17552,38 @@
 version of the system. It should not be used.
 
 \ENDDOC
+\DOC{NO\_CONV}
+
+\TYPE {\small\verb%NO_CONV : conv%}\egroup
+
+\SYNOPSIS
+Conversion that always fails.
+
+\FAILURE
+{\small\verb%NO_CONV%} always fails.
+
+\SEEALSO
+ALL_CONV.
+
+\ENDDOC
+\DOC{NO\_TAC}
+
+\TYPE {\small\verb%NO_TAC : tactic%}\egroup
+
+\SYNOPSIS
+Tactic which always fails.
+
+\DESCRIBE
+Whatever goal it is applied to, {\small\verb%NO_TAC%} always fails
+with string {\small\verb%`NO_TAC`%}.
+
+\FAILURE
+Always fails.
+
+\SEEALSO
+ALL_TAC, ALL_THEN, FAIL_TAC, NO_THEN.
+
+\ENDDOC
 \DOC{not}
 
 \TYPE {\small\verb%$not : (bool -> bool)%}\egroup
@@ -17660,7 +17690,29 @@
 Fails if applied to a term not of the form {\small\verb%~(!x.P)%}.
 
 \SEEALSO
-EXISTS_NOT_CONV, FORALL_NOT_CONV, NOT_EXISTS_CONV.
+EXISTS_NOT_CONV, FORALL_NOT_CONV, NOT_EXISTS_CONV.
+
+\ENDDOC
+\DOC{NO\_THEN}
+
+\TYPE {\small\verb%NO_THEN : thm_tactical%}\egroup
+
+\SYNOPSIS
+Theorem-tactical which always fails.
+
+\DESCRIBE
+When applied to a theorem-tactic and a theorem, the theorem-tactical
+{\small\verb%NO_THEN%} always fails with string {\small\verb%`NO_THEN`%}.
+
+\FAILURE
+Always fails when applied to a theorem-tactic and a theorem (note that it
+never gets as far as being applied to a goal!)
+
+\USES
+Writing compound tactics or tacticals.
+
+\SEEALSO
+ALL_TAC, ALL_THEN, FAIL_TAC, NO_TAC.
 
 \ENDDOC
 \DOC{NOT\_INTRO}
@@ -17733,58 +17785,13 @@
 MP, EQ_MP, LIST_MP, MATCH_MP, MATCH_MP_TAC, MP_TAC.
 
 \ENDDOC
-\DOC{NO\_CONV}
-
-\TYPE {\small\verb%NO_CONV : conv%}\egroup
-
-\SYNOPSIS
-Conversion that always fails.
-
-\FAILURE
-{\small\verb%NO_CONV%} always fails.
-
-\SEEALSO
-ALL_CONV.
-
-\ENDDOC
-\DOC{NO\_TAC}
-
-\TYPE {\small\verb%NO_TAC : tactic%}\egroup
-
-\SYNOPSIS
-Tactic which always fails.
-
-\DESCRIBE
-Whatever goal it is applied to, {\small\verb%NO_TAC%} always fails
-with string {\small\verb%`NO_TAC`%}.
-
-\FAILURE
-Always fails.
-
-\SEEALSO
-ALL_TAC, ALL_THEN, FAIL_TAC, NO_THEN.
-
-\ENDDOC
-\DOC{NO\_THEN}
+\DOC{n\_strip\_quant}
 
-\TYPE {\small\verb%NO_THEN : thm_tactical%}\egroup
+\TYPE {\small\verb%n_strip_quant : ((* -> (** # *)) -> int -> * -> (** list # *))%}\egroup
 
 \SYNOPSIS
-Theorem-tactical which always fails.
-
-\DESCRIBE
-When applied to a theorem-tactic and a theorem, the theorem-tactical
-{\small\verb%NO_THEN%} always fails with string {\small\verb%`NO_THEN`%}.
-
-\FAILURE
-Always fails when applied to a theorem-tactic and a theorem (note that it
-never gets as far as being applied to a goal!)
-
-\USES
-Writing compound tactics or tacticals.
-
-\SEEALSO
-ALL_TAC, ALL_THEN, FAIL_TAC, NO_TAC.
+This function is for internal use only and is to be deleted from a future
+version of the system. It should not be used.
 
 \ENDDOC
 \DOC{null}
@@ -17883,15 +17890,6 @@
 \end{verbatim}
 }
 \ENDDOC
-\DOC{n\_strip\_quant}
-
-\TYPE {\small\verb%n_strip_quant : ((* -> (** # *)) -> int -> * -> (** list # *))%}\egroup
-
-\SYNOPSIS
-This function is for internal use only and is to be deleted from a future
-version of the system. It should not be used.
-
-\ENDDOC
 \DOC{o}
 
 \TYPE {\small\verb%$o : (((* -> **) # (*** -> *)) -> *** -> **)%}\egroup
@@ -18063,6 +18061,71 @@
 DEPTH_CONV, REDEPTH_CONV, TOP_DEPTH_CONV, ONCE_REW_DEPTH_CONV.
 
 \ENDDOC
+\DOC{ONCE\_REW\_DEPTH\_CONV}
+
+\TYPE {\small\verb%ONCE_REW_DEPTH_CONV : (conv -> conv)%}\egroup
+
+\SYNOPSIS
+Applies a conversion once to the first suitable sub-term(s) encountered in
+top-down order. For use in rewriting.
+
+\DESCRIBE
+{\small\verb%ONCE_REW_DEPTH_CONV c tm%} applies the conversion {\small\verb%c%} once to the first
+subterm or subterms encountered in a top-down `parallel' search of the term
+{\small\verb%tm%} for which {\small\verb%c%} succeeds.  If the conversion {\small\verb%c%} fails on all subterms of
+{\small\verb%tm%}, the theorem returned is {\small\verb%|- tm = tm%}.
+
+{\small\verb%ONCE_REW_DEPTH_CONV%} is a special version of {\small\verb%ONCE_DEPTH_CONV%} for use by the
+rewriting conversions, rules and tactics. It differs from {\small\verb%ONCE_DEPTH_CONV%} as
+follows: If converting an abstraction fails due to the presence of the bound
+variable in the hypotheses of the theorem generated by converting the body,
+{\small\verb%ONCE_REW_DEPTH_CONV%} retries the conversion having renamed the bound variable
+of the abstraction. If successful the renaming is reversed.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+The following example illustrates the difference between the functions
+{\small\verb%ONCE_REW_DEPTH_CONV%} and {\small\verb%ONCE_DEPTH_CONV%}. It is not intended to illustrate
+the full range of behaviour of the former. Both {\small\verb%ONCE_REW_DEPTH_CONV%} and
+{\small\verb%ONCE_DEPTH_CONV%} successfully apply the theorem {\small\verb%ADD_0%} inside an abstraction:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #ONCE_REW_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
+   |- (\n. n + 0) = (\n. n)
+
+   #ONCE_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
+   |- (\n. n + 0) = (\n. n)
+\end{verbatim}
+}
+\noindent However, if a hypothesis containing a free occurrence of the bound
+variable is added to the rewrite rule, it interferes with the operation of
+{\small\verb%ONCE_DEPTH_CONV%} but not that of {\small\verb%ONCE_REW_DEPTH_CONV%}:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #let th = ADD_ASSUM "n = 0" ADD_0;;
+   th = n = 0 |- !m. m + 0 = m
+
+   #ONCE_REW_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
+   n = 0 |- (\n. n + 0) = (\n. n)
+
+   #ONCE_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
+   |- (\n. n + 0) = (\n. n + 0)
+\end{verbatim}
+}
+\COMMENTS
+The implementation of this function uses failure to avoid rebuilding
+unchanged subterms. That is to say, during execution the failure string
+{\small\verb%`QCONV`%} may be generated and later trapped. The behaviour of the function
+is dependent on this use of failure. So, if the conversion given as argument
+happens to generate a failure with string {\small\verb%`QCONV`%}, the operation of
+{\small\verb%ONCE_REW_DEPTH_CONV%} will be unpredictable.
+
+\SEEALSO
+REW_DEPTH_CONV, ONCE_DEPTH_CONV.
+
+\ENDDOC
 \DOC{ONCE\_REWRITE\_CONV}
 
 \TYPE {\small\verb%ONCE_REWRITE_CONV : (thm list -> conv)%}\egroup
@@ -18176,71 +18239,6 @@
 PURE_ONCE_REWRITE_TAC, PURE_REWRITE_TAC, REWRITE_TAC, SUBST_TAC.
 
 \ENDDOC
-\DOC{ONCE\_REW\_DEPTH\_CONV}
-
-\TYPE {\small\verb%ONCE_REW_DEPTH_CONV : (conv -> conv)%}\egroup
-
-\SYNOPSIS
-Applies a conversion once to the first suitable sub-term(s) encountered in
-top-down order. For use in rewriting.
-
-\DESCRIBE
-{\small\verb%ONCE_REW_DEPTH_CONV c tm%} applies the conversion {\small\verb%c%} once to the first
-subterm or subterms encountered in a top-down `parallel' search of the term
-{\small\verb%tm%} for which {\small\verb%c%} succeeds.  If the conversion {\small\verb%c%} fails on all subterms of
-{\small\verb%tm%}, the theorem returned is {\small\verb%|- tm = tm%}.
-
-{\small\verb%ONCE_REW_DEPTH_CONV%} is a special version of {\small\verb%ONCE_DEPTH_CONV%} for use by the
-rewriting conversions, rules and tactics. It differs from {\small\verb%ONCE_DEPTH_CONV%} as
-follows: If converting an abstraction fails due to the presence of the bound
-variable in the hypotheses of the theorem generated by converting the body,
-{\small\verb%ONCE_REW_DEPTH_CONV%} retries the conversion having renamed the bound variable
-of the abstraction. If successful the renaming is reversed.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-The following example illustrates the difference between the functions
-{\small\verb%ONCE_REW_DEPTH_CONV%} and {\small\verb%ONCE_DEPTH_CONV%}. It is not intended to illustrate
-the full range of behaviour of the former. Both {\small\verb%ONCE_REW_DEPTH_CONV%} and
-{\small\verb%ONCE_DEPTH_CONV%} successfully apply the theorem {\small\verb%ADD_0%} inside an abstraction:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #ONCE_REW_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
-   |- (\n. n + 0) = (\n. n)
-
-   #ONCE_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
-   |- (\n. n + 0) = (\n. n)
-\end{verbatim}
-}
-\noindent However, if a hypothesis containing a free occurrence of the bound
-variable is added to the rewrite rule, it interferes with the operation of
-{\small\verb%ONCE_DEPTH_CONV%} but not that of {\small\verb%ONCE_REW_DEPTH_CONV%}:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #let th = ADD_ASSUM "n = 0" ADD_0;;
-   th = n = 0 |- !m. m + 0 = m
-
-   #ONCE_REW_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
-   n = 0 |- (\n. n + 0) = (\n. n)
-
-   #ONCE_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
-   |- (\n. n + 0) = (\n. n + 0)
-\end{verbatim}
-}
-\COMMENTS
-The implementation of this function uses failure to avoid rebuilding
-unchanged subterms. That is to say, during execution the failure string
-{\small\verb%`QCONV`%} may be generated and later trapped. The behaviour of the function
-is dependent on this use of failure. So, if the conversion given as argument
-happens to generate a failure with string {\small\verb%`QCONV`%}, the operation of
-{\small\verb%ONCE_REW_DEPTH_CONV%} will be unpredictable.
-
-\SEEALSO
-REW_DEPTH_CONV, ONCE_DEPTH_CONV.
-
-\ENDDOC
 \DOC{oo}
 
 \TYPE {\small\verb%$oo : ((((* # **) -> ***) # (**** -> *) # (**** -> **)) -> **** -> ***)%}\egroup
@@ -18311,43 +18309,43 @@
 close, openi, read, write
 
 \ENDDOC
-\DOC{ORELSE}
+\DOC{ORELSEC}
 
-\TYPE {\small\verb%$ORELSE : (tactic -> tactic -> tactic)%}\egroup
+\TYPE {\small\verb%$ORELSEC : (conv -> conv -> conv)%}\egroup
 
 \SYNOPSIS
-Applies first tactic, and iff it fails, applies the second instead.
+Applies the first of two conversions that succeeds.
 
 \DESCRIBE
-If {\small\verb%T1%} and {\small\verb%T2%} are tactics, {\small\verb%T1 ORELSE T2%} is a tactic which applies {\small\verb%T1%} to
-a goal, and iff it fails, applies {\small\verb%T2%} to the goal instead.
+{\small\verb%(c1 ORELSEC c2) "t"%} returns the result of applying the conversion {\small\verb%c1%} to
+the term {\small\verb%"t"%} if this succeeds.  Otherwise {\small\verb%(c1 ORELSEC c2) "t"%} returns the
+result of applying the conversion {\small\verb%c2%} to the term {\small\verb%"t"%}.
 
 \FAILURE
-The application of {\small\verb%ORELSE%} to a pair of tactics never fails.
-The resulting tactic fails if both {\small\verb%T1%} and {\small\verb%T2%} fail when applied to the
-relevant goal.
+{\small\verb%(c1 ORELSEC c2) "t"%} fails both {\small\verb%c1%} and {\small\verb%c2%}  fail when applied to {\small\verb%"t"%}.
 
 \SEEALSO
-EVERY, FIRST, THEN.
+FIRST_CONV.
 
 \ENDDOC
-\DOC{ORELSEC}
+\DOC{ORELSE}
 
-\TYPE {\small\verb%$ORELSEC : (conv -> conv -> conv)%}\egroup
+\TYPE {\small\verb%$ORELSE : (tactic -> tactic -> tactic)%}\egroup
 
 \SYNOPSIS
-Applies the first of two conversions that succeeds.
+Applies first tactic, and iff it fails, applies the second instead.
 
 \DESCRIBE
-{\small\verb%(c1 ORELSEC c2) "t"%} returns the result of applying the conversion {\small\verb%c1%} to
-the term {\small\verb%"t"%} if this succeeds.  Otherwise {\small\verb%(c1 ORELSEC c2) "t"%} returns the
-result of applying the conversion {\small\verb%c2%} to the term {\small\verb%"t"%}.
+If {\small\verb%T1%} and {\small\verb%T2%} are tactics, {\small\verb%T1 ORELSE T2%} is a tactic which applies {\small\verb%T1%} to
+a goal, and iff it fails, applies {\small\verb%T2%} to the goal instead.
 
 \FAILURE
-{\small\verb%(c1 ORELSEC c2) "t"%} fails both {\small\verb%c1%} and {\small\verb%c2%}  fail when applied to {\small\verb%"t"%}.
+The application of {\small\verb%ORELSE%} to a pair of tactics never fails.
+The resulting tactic fails if both {\small\verb%T1%} and {\small\verb%T2%} fail when applied to the
+relevant goal.
 
 \SEEALSO
-FIRST_CONV.
+EVERY, FIRST, THEN.
 
 \ENDDOC
 \DOC{ORELSE\_TCL}
@@ -18482,29 +18480,6 @@
 outl, inl, inr, isl
 
 \ENDDOC
-\DOC{p}
-
-\TYPE {\small\verb%p : (int -> void)%}\egroup
-
-\SYNOPSIS
-Prints the top levels of the subgoal package goal stack.
-
-\DESCRIBE
-The function {\small\verb%p%} is part of the subgoal package. It is an abbreviation for the
-function {\small\verb%print_state%}. For a description of the subgoal package, see
-{\small\verb%set_goal%}.
-
-\FAILURE
-Never fails.
-
-\USES
-Examining the proof state during an interactive proof session.
-
-\SEEALSO
-b, backup, backup_limit, e, expand, expandf, g, get_state, print_state, r,
-rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
-
-\ENDDOC
 \DOC{pair}
 
 \TYPE {\small\verb%pair : (* -> ** -> (* # **))%}\egroup
@@ -18878,7 +18853,30 @@
 quantifier), and matches it to {\small\verb%T%}.
 
 \SEEALSO
-INST_TYPE, INST_TY_TERM, match.
+INST_TYPE, INST_TY_TERM, match.
+
+\ENDDOC
+\DOC{p}
+
+\TYPE {\small\verb%p : (int -> void)%}\egroup
+
+\SYNOPSIS
+Prints the top levels of the subgoal package goal stack.
+
+\DESCRIBE
+The function {\small\verb%p%} is part of the subgoal package. It is an abbreviation for the
+function {\small\verb%print_state%}. For a description of the subgoal package, see
+{\small\verb%set_goal%}.
+
+\FAILURE
+Never fails.
+
+\USES
+Examining the proof state during an interactive proof session.
+
+\SEEALSO
+b, backup, backup_limit, e, expand, expandf, g, get_state, print_state, r,
+rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
 
 \ENDDOC
 \DOC{POP\_ASSUM}
@@ -20153,56 +20151,6 @@
 set_prompt.
 
 \ENDDOC
-\DOC{PROVE}
-
-\TYPE {\small\verb%PROVE : ((term # tactic) -> thm)%}\egroup
-
-\SYNOPSIS
-Attempts to prove a boolean term using the supplied tactic.
-
-\DESCRIBE
-When applied to a term-tactic pair {\small\verb%(tm,tac)%}, the function {\small\verb%PROVE%} attempts to
-prove the goal {\small\verb%?- tm%}, that is, the term {\small\verb%tm%} with no assumptions, using the
-tactic {\small\verb%tac%}. If {\small\verb%PROVE%} succeeds, it returns the corresponding theorem
-{\small\verb%A |- tm%}, where the assumption list {\small\verb%A%} may not be empty if the tactic is
-invalid; {\small\verb%PROVE%} has no inbuilt validity-checking.
-
-\FAILURE
-Fails if the term is not of type {\small\verb%bool%} (and so cannot possibly be
-the conclusion of a theorem), or if the tactic cannot solve the goal.
-In the latter case {\small\verb%PROVE%} will list the unsolved goals to help the user.
-
-\SEEALSO
-TAC_PROOF, prove, prove_thm, VALID.
-
-\ENDDOC
-\DOC{prove}
-
-\TYPE {\small\verb%prove : ((term # tactic) -> thm)%}\egroup
-
-\SYNOPSIS
-Attempts to prove a boolean term using the supplied tactic.
-
-\DESCRIBE
-When applied to a term-tactic pair {\small\verb%(tm,tac)%}, the function {\small\verb%prove%} attempts to
-prove the goal {\small\verb%?- tm%}, that is, the term {\small\verb%tm%} with no assumptions, using the
-tactic {\small\verb%tac%}. If {\small\verb%prove%} succeeds, it returns the corresponding theorem
-{\small\verb%A |- tm%}, where the assumption list {\small\verb%A%} may not be empty if the tactic is
-invalid; {\small\verb%prove%} has no inbuilt validity-checking.
-
-\FAILURE
-Fails if the term is not of type {\small\verb%bool%} (and so cannot possibly be
-the conclusion of a theorem), or if the tactic cannot solve the goal.
-
-\COMMENTS
-The function {\small\verb%PROVE%} provides almost identical functionality, and will
-also list unsolved goals if the tactic fails. It is therefore preferable
-for most purposes.
-
-\SEEALSO
-PROVE, prove_thm, TAC_PROOF, VALID.
-
-\ENDDOC
 \DOC{prove\_abs\_fn\_one\_one}
 
 \TYPE {\small\verb%prove_abs_fn_one_one : (thm -> thm)%}\egroup
@@ -20398,6 +20346,56 @@
 prove_constructors_distinct, prove_induction_thm, prove_rec_fn_exists.
 
 \ENDDOC
+\DOC{prove}
+
+\TYPE {\small\verb%prove : ((term # tactic) -> thm)%}\egroup
+
+\SYNOPSIS
+Attempts to prove a boolean term using the supplied tactic.
+
+\DESCRIBE
+When applied to a term-tactic pair {\small\verb%(tm,tac)%}, the function {\small\verb%prove%} attempts to
+prove the goal {\small\verb%?- tm%}, that is, the term {\small\verb%tm%} with no assumptions, using the
+tactic {\small\verb%tac%}. If {\small\verb%prove%} succeeds, it returns the corresponding theorem
+{\small\verb%A |- tm%}, where the assumption list {\small\verb%A%} may not be empty if the tactic is
+invalid; {\small\verb%prove%} has no inbuilt validity-checking.
+
+\FAILURE
+Fails if the term is not of type {\small\verb%bool%} (and so cannot possibly be
+the conclusion of a theorem), or if the tactic cannot solve the goal.
+
+\COMMENTS
+The function {\small\verb%PROVE%} provides almost identical functionality, and will
+also list unsolved goals if the tactic fails. It is therefore preferable
+for most purposes.
+
+\SEEALSO
+PROVE, prove_thm, TAC_PROOF, VALID.
+
+\ENDDOC
+\DOC{PROVE}
+
+\TYPE {\small\verb%PROVE : ((term # tactic) -> thm)%}\egroup
+
+\SYNOPSIS
+Attempts to prove a boolean term using the supplied tactic.
+
+\DESCRIBE
+When applied to a term-tactic pair {\small\verb%(tm,tac)%}, the function {\small\verb%PROVE%} attempts to
+prove the goal {\small\verb%?- tm%}, that is, the term {\small\verb%tm%} with no assumptions, using the
+tactic {\small\verb%tac%}. If {\small\verb%PROVE%} succeeds, it returns the corresponding theorem
+{\small\verb%A |- tm%}, where the assumption list {\small\verb%A%} may not be empty if the tactic is
+invalid; {\small\verb%PROVE%} has no inbuilt validity-checking.
+
+\FAILURE
+Fails if the term is not of type {\small\verb%bool%} (and so cannot possibly be
+the conclusion of a theorem), or if the tactic cannot solve the goal.
+In the latter case {\small\verb%PROVE%} will list the unsolved goals to help the user.
+
+\SEEALSO
+TAC_PROOF, prove, prove_thm, VALID.
+
+\ENDDOC
 \DOC{PROVE\_HYP}
 
 \TYPE {\small\verb%PROVE_HYP : (thm -> thm -> thm)%}\egroup
@@ -20940,45 +20938,6 @@
 Never fails.
 
 \ENDDOC
-\DOC{r}
-
-\TYPE {\small\verb%r : (int -> void)%}\egroup
-
-\SYNOPSIS
-Reorders the subgoals on top of the subgoal package goal stack.
-
-\DESCRIBE
-The function {\small\verb%r%} is part of the subgoal package. It  is an abbreviation for
-{\small\verb%rotate%}. For a description of the subgoal package, see  {\small\verb%set_goal%}.
-
-\FAILURE
-As for {\small\verb%rotate%}.
-
-\USES
-Proving subgoals in a different order to that generated by the subgoal package.
-
-\SEEALSO
-b, backup, backup_limit, e, expand, expandf, g, get_state, p, print_state,
-rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
-
-\ENDDOC
-\DOC{rand}
-
-\TYPE {\small\verb%rand : (term -> term)%}\egroup
-
-\SYNOPSIS
-Returns the operand from a combination (function application).
-
-\DESCRIBE
-{\small\verb%rand "t1 t2"%} returns {\small\verb%"t2"%}.
-
-\FAILURE
-Fails with {\small\verb%rand%} if term is not a combination.
-
-\SEEALSO
-rator, dest_comb.
-
-\ENDDOC
 \DOC{RAND\_CONV}
 
 \TYPE {\small\verb%RAND_CONV : (conv -> conv)%}\egroup
@@ -21016,21 +20975,21 @@
 ABS_CONV, RATOR_CONV, SUB_CONV.
 
 \ENDDOC
-\DOC{rator}
+\DOC{rand}
 
-\TYPE {\small\verb%rator : (term -> term)%}\egroup
+\TYPE {\small\verb%rand : (term -> term)%}\egroup
 
 \SYNOPSIS
-Returns the operator from a combination (function application).
+Returns the operand from a combination (function application).
 
 \DESCRIBE
-{\small\verb%rator("t1 t2")%} returns {\small\verb%"t1"%}.
+{\small\verb%rand "t1 t2"%} returns {\small\verb%"t2"%}.
 
 \FAILURE
-Fails with {\small\verb%rator%} if term is not a combination.
+Fails with {\small\verb%rand%} if term is not a combination.
 
 \SEEALSO
-rand, dest_comb.
+rator, dest_comb.
 
 \ENDDOC
 \DOC{RATOR\_CONV}
@@ -21070,6 +21029,45 @@
 ABS_CONV, RAND_CONV, SUB_CONV.
 
 \ENDDOC
+\DOC{rator}
+
+\TYPE {\small\verb%rator : (term -> term)%}\egroup
+
+\SYNOPSIS
+Returns the operator from a combination (function application).
+
+\DESCRIBE
+{\small\verb%rator("t1 t2")%} returns {\small\verb%"t1"%}.
+
+\FAILURE
+Fails with {\small\verb%rator%} if term is not a combination.
+
+\SEEALSO
+rand, dest_comb.
+
+\ENDDOC
+\DOC{r}
+
+\TYPE {\small\verb%r : (int -> void)%}\egroup
+
+\SYNOPSIS
+Reorders the subgoals on top of the subgoal package goal stack.
+
+\DESCRIBE
+The function {\small\verb%r%} is part of the subgoal package. It  is an abbreviation for
+{\small\verb%rotate%}. For a description of the subgoal package, see  {\small\verb%set_goal%}.
+
+\FAILURE
+As for {\small\verb%rotate%}.
+
+\USES
+Proving subgoals in a different order to that generated by the subgoal package.
+
+\SEEALSO
+b, backup, backup_limit, e, expand, expandf, g, get_state, p, print_state,
+rotate, save_top_thm, set_goal, set_state, top_goal, top_thm.
+
+\ENDDOC
 \DOC{read}
 
 \TYPE {\small\verb%read : (string -> string)%}\egroup
@@ -21091,63 +21089,26 @@
 \EXAMPLE
 The following assumes that HOL is being run under Unix. It will overwrite an
 existing file {\small\verb%test-file%} in the current directory. Notice that the actual
-string returned by {\small\verb%openi%} may vary on other systems.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #system `echo "Hi" >test-file`;;
-   0 : int
-
-   #let port = openi `test-file`;;
-   port = `%test-file` : string
-
-   #read port, read port, read port, read port, read port;;
-   (`H`, `i`, `
-   `, `nil`, `nil`)
-   : (string # string # string # string # string)
-
-   #close port;;
-   () : void
-\end{verbatim}
-}
-\SEEALSO
-append_openw, close, openi, openw, tty_read, tty_write, write.
-
-\ENDDOC
-\DOC{RecordStep}
-
-\TYPE {\small\verb%RecordStep : step -> void%}\egroup
-
-
-\SYNOPSIS
-Record a single inference step.
-
-\DESCRIBE
-A proof is a list of inference steps. After the proof recorder is
-enabled, every inference performed by the system is recorded and
-cumulated in an internal buffer. When a proof is completed, the raw
-records can then be processed and output to a disk file.
-
-{\small\verb%record_proof%} is a system function for recording a single proof step.
-The type {\small\verb%step%} represents a basic inference step. It contains all
-the necessary information of each inference. There are currently 52
-basic inferences which are being recorded. All other ML functions
-representing inference rules are implemented by these basic
-inferences.
-If the proof recorder is enabled when an inference is performed, 
-{\small\verb%RecordStep%} will add a step into the internal buffer. 
+string returned by {\small\verb%openi%} may vary on other systems.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #system `echo "Hi" >test-file`;;
+   0 : int
 
-\FAILURE
-Never fail.
+   #let port = openi `test-file`;;
+   port = `%test-file` : string
 
-\COMMENTS
-This is a system function implementing the proof recorded. Users
-should not use this function directly. User functions are provided in
-the library {\small\verb%record_proof%}.  When new basic inference rule
-is implemented, this function should be called to record the inference step.
+   #read port, read port, read port, read port, read port;;
+   (`H`, `i`, `
+   `, `nil`, `nil`)
+   : (string # string # string # string # string)
 
+   #close port;;
+   () : void
+\end{verbatim}
+}
 \SEEALSO
-record_proof, is_recording_proof, get_steps,
-suspend_recording, resume_recording.
+append_openw, close, openi, openw, tty_read, tty_write, write.
 
 \ENDDOC
 \DOC{record\_proof}
@@ -21225,6 +21186,43 @@
 TAC_PROOF, PROVE, prove, prove_thm.
 
 \ENDDOC
+\DOC{RecordStep}
+
+\TYPE {\small\verb%RecordStep : step -> void%}\egroup
+
+
+\SYNOPSIS
+Record a single inference step.
+
+\DESCRIBE
+A proof is a list of inference steps. After the proof recorder is
+enabled, every inference performed by the system is recorded and
+cumulated in an internal buffer. When a proof is completed, the raw
+records can then be processed and output to a disk file.
+
+{\small\verb%record_proof%} is a system function for recording a single proof step.
+The type {\small\verb%step%} represents a basic inference step. It contains all
+the necessary information of each inference. There are currently 52
+basic inferences which are being recorded. All other ML functions
+representing inference rules are implemented by these basic
+inferences.
+If the proof recorder is enabled when an inference is performed, 
+{\small\verb%RecordStep%} will add a step into the internal buffer. 
+
+\FAILURE
+Never fail.
+
+\COMMENTS
+This is a system function implementing the proof recorded. Users
+should not use this function directly. User functions are provided in
+the library {\small\verb%record_proof%}.  When new basic inference rule
+is implemented, this function should be called to record the inference step.
+
+\SEEALSO
+record_proof, is_recording_proof, get_steps,
+suspend_recording, resume_recording.
+
+\ENDDOC
 \DOC{REDEPTH\_CONV}
 
 \TYPE {\small\verb%REDEPTH_CONV : (conv -> conv)%}\egroup
@@ -21373,25 +21371,6 @@
 set_sticky_type, sticky_list.
 
 \ENDDOC
-\DOC{REPEAT}
-
-\TYPE {\small\verb%REPEAT : (tactic -> tactic)%}\egroup
-
-\SYNOPSIS
-Repeatedly applies a tactic until it fails.
-
-\DESCRIBE
-The tactic {\small\verb%REPEAT T%} is a tactic which applies {\small\verb%T%} to a goal, and while it
-succeeds, continues applying it to all subgoals generated.
-
-\FAILURE
-The application of {\small\verb%REPEAT%} to a tactic never fails, and neither does the
-composite tactic, even if the basic tactic fails immediately.
-
-\SEEALSO
-EVERY, FIRST, ORELSE, THEN, THENL.
-
-\ENDDOC
 \DOC{REPEATC}
 
 \TYPE {\small\verb%REPEATC : (conv -> conv)%}\egroup
@@ -21412,6 +21391,25 @@
 Never fails, but can diverge if the supplied conversion never fails.
 
 \ENDDOC
+\DOC{REPEAT}
+
+\TYPE {\small\verb%REPEAT : (tactic -> tactic)%}\egroup
+
+\SYNOPSIS
+Repeatedly applies a tactic until it fails.
+
+\DESCRIBE
+The tactic {\small\verb%REPEAT T%} is a tactic which applies {\small\verb%T%} to a goal, and while it
+succeeds, continues applying it to all subgoals generated.
+
+\FAILURE
+The application of {\small\verb%REPEAT%} to a tactic never fails, and neither does the
+composite tactic, even if the basic tactic fails immediately.
+
+\SEEALSO
+EVERY, FIRST, ORELSE, THEN, THENL.
+
+\ENDDOC
 \DOC{REPEAT\_GTCL}
 
 \TYPE {\small\verb%REPEAT_GTCL : (thm_tactical -> thm_tactical)%}\egroup
@@ -21492,20 +21490,6 @@
 REPEAT_GTCL, THEN_TCL.
 
 \ENDDOC
-\DOC{replicate}
-
-\TYPE {\small\verb%replicate : (* -> int -> * list)%}\egroup
-
-\SYNOPSIS
-Makes a list consisting of a value replicated a specified number of times.
-
-\DESCRIBE
-{\small\verb%replicate x n%} returns {\small\verb%[x;...;x]%}, a list of length {\small\verb%n%}.
-
-\FAILURE
-Fails if number of replications is less than zero.
-
-\ENDDOC
 \DOC{rep\_goals}
 
 \TYPE {\small\verb%rep_goals : (goalstack -> subgoals list)%}\egroup
@@ -21515,43 +21499,18 @@
 version of the system. It should not be used.
 
 \ENDDOC
-\DOC{resume\_recording}
-
-\TYPE {\small\verb%resume_recording : void -> void%}\egroup
+\DOC{replicate}
 
+\TYPE {\small\verb%replicate : (* -> int -> * list)%}\egroup
 
 \SYNOPSIS
-Suspend proof recording temporarily.
+Makes a list consisting of a value replicated a specified number of times.
 
 \DESCRIBE
-A proof is a list of inference steps. After the proof recorder is
-enabled, every inference performed by the system is recorded and
-cumulated in an internal buffer. When a proof is completed, the raw
-records can then be processed and output to a disk file.
-
-{\small\verb%resume_recording%} is a low level user function for managing the proof
-recorder. It resumes the proof recorder without clearing the internal
-inference step buffer.  The proof recorder should be in the suspended state.
-Otherwise, this function does nothing.
-
-The current state of the proof recorder can interrogated using the
-function {\small\verb%is_recording_proof%}. A value of {\small\verb%false%} indicates the proof
-recorder is disabled.
+{\small\verb%replicate x n%} returns {\small\verb%[x;...;x]%}, a list of length {\small\verb%n%}.
 
 \FAILURE
-Never fail.
-
-\COMMENTS
-This function is used to implement higher level user functions for
-recording proof in the library {\small\verb%record_proof%}. It is much more
-convenient to use those functions than the low level functions
-such as {\small\verb%resume_recording%} directly.
-
-\SEEALSO
-record_proof, is_recording_proof, RecordStep, get_steps, suspend_recording,
-current_proof, current_proof_file,
-new_proof_file, close_proof_file, begin_proof, end_proof,
-TAC_PROOF, PROVE, prove, prove_thm.
+Fails if number of replications is less than zero.
 
 \ENDDOC
 \DOC{RES\_CANON}
@@ -21757,60 +21716,126 @@
 implications used for resolution are taken from the assumptions of the goal
 itself, rather than supplied as an argument.
 
-When applied to a goal {\small\verb%A ?- g%}, the tactic {\small\verb%RES_THEN ttac%} uses {\small\verb%RES_CANON%} to
-obtain a set of implicative theorems in canonical form from the assumptions {\small\verb%A%}
-of the goal. Each of the resulting theorems (if there are any) will have the
-form:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ai |- !x1...xn. ui ==> vi
-\end{verbatim}
-}
-\noindent where {\small\verb%ai%} is one of the assumptions of the goal. Having obtained
-these implications, {\small\verb%RES_THEN%} then attempts to match each antecedent {\small\verb%ui%} to
-each assumption {\small\verb%aj |- aj%} in the assumptions {\small\verb%A%}.  If the antecedent {\small\verb%ui%} of
-any implication matches the conclusion {\small\verb%aj%} of any assumption, then an instance
-of the theorem {\small\verb%ai, aj |- vi%}, called a `resolvent', is obtained by
-specialization of the variables {\small\verb%x1%}, ..., {\small\verb%xn%} and type instantiation,
-followed by an application of modus ponens.  There may be more than one
-canonical implication derivable from the assumptions of the goal and each
-such implication is tried against every assumption, so there may be several
-resolvents (or, indeed, none).
+When applied to a goal {\small\verb%A ?- g%}, the tactic {\small\verb%RES_THEN ttac%} uses {\small\verb%RES_CANON%} to
+obtain a set of implicative theorems in canonical form from the assumptions {\small\verb%A%}
+of the goal. Each of the resulting theorems (if there are any) will have the
+form:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   ai |- !x1...xn. ui ==> vi
+\end{verbatim}
+}
+\noindent where {\small\verb%ai%} is one of the assumptions of the goal. Having obtained
+these implications, {\small\verb%RES_THEN%} then attempts to match each antecedent {\small\verb%ui%} to
+each assumption {\small\verb%aj |- aj%} in the assumptions {\small\verb%A%}.  If the antecedent {\small\verb%ui%} of
+any implication matches the conclusion {\small\verb%aj%} of any assumption, then an instance
+of the theorem {\small\verb%ai, aj |- vi%}, called a `resolvent', is obtained by
+specialization of the variables {\small\verb%x1%}, ..., {\small\verb%xn%} and type instantiation,
+followed by an application of modus ponens.  There may be more than one
+canonical implication derivable from the assumptions of the goal and each
+such implication is tried against every assumption, so there may be several
+resolvents (or, indeed, none).
+
+Tactics are produced using the theorem-tactic {\small\verb%ttac%} from all these resolvents
+(failures of {\small\verb%ttac%} at this stage are filtered out) and these tactics are then
+applied in an unspecified sequence to the goal.  That is,
+{\par\samepage\setseps\small
+\begin{verbatim}
+   RES_THEN ttac (A ?- g)
+\end{verbatim}
+}
+\noindent has the effect of:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   MAP_EVERY (mapfilter ttac [... ; (ai,aj |- vi) ; ...]) (A ?- g)
+\end{verbatim}
+}
+\noindent where the theorems {\small\verb%ai,aj |- vi%} are all the consequences that can be
+drawn by a (single) matching modus-ponens inference from the assumptions {\small\verb%A%}
+and the implications derived using {\small\verb%RES_CANON%} from the assumptions.  The
+sequence in which the theorems {\small\verb%ai,aj |- vi%} are generated and the
+corresponding tactics applied is unspecified.
+
+\FAILURE
+Evaluating {\small\verb%RES_THEN ttac th%} fails with `{\small\verb%no implication%}' if no
+implication(s) can be derived from the assumptions of the goal by the
+transformation process described under the entry for {\small\verb%RES_CANON%}.  Evaluating
+{\small\verb%RES_THEN ttac (A ?- g)%} fails with `{\small\verb%no resolvents%}' if no assumption of the
+goal {\small\verb%A ?- g%} can be resolved with the derived implication or implications.
+Evaluation also fails, with `{\small\verb%no tactics%}', if there are resolvents, but for
+every resolvent {\small\verb%ai,aj |- vi%} evaluating the application {\small\verb%ttac (ai,aj |- vi)%}
+fails---that is, if for every resolvent {\small\verb%ttac%} fails to produce a tactic.
+Finally, failure is propagated if any of the tactics that are produced from the
+resolvents by {\small\verb%ttac%} fails when applied in sequence to the goal.
+
+\SEEALSO
+IMP_RES_TAC, IMP_RES_THEN, MATCH_MP, RES_CANON, RES_TAC.
+
+\ENDDOC
+\DOC{resume\_recording}
+
+\TYPE {\small\verb%resume_recording : void -> void%}\egroup
+
+
+\SYNOPSIS
+Suspend proof recording temporarily.
+
+\DESCRIBE
+A proof is a list of inference steps. After the proof recorder is
+enabled, every inference performed by the system is recorded and
+cumulated in an internal buffer. When a proof is completed, the raw
+records can then be processed and output to a disk file.
+
+{\small\verb%resume_recording%} is a low level user function for managing the proof
+recorder. It resumes the proof recorder without clearing the internal
+inference step buffer.  The proof recorder should be in the suspended state.
+Otherwise, this function does nothing.
+
+The current state of the proof recorder can interrogated using the
+function {\small\verb%is_recording_proof%}. A value of {\small\verb%false%} indicates the proof
+recorder is disabled.
+
+\FAILURE
+Never fail.
+
+\COMMENTS
+This function is used to implement higher level user functions for
+recording proof in the library {\small\verb%record_proof%}. It is much more
+convenient to use those functions than the low level functions
+such as {\small\verb%resume_recording%} directly.
+
+\SEEALSO
+record_proof, is_recording_proof, RecordStep, get_steps, suspend_recording,
+current_proof, current_proof_file,
+new_proof_file, close_proof_file, begin_proof, end_proof,
+TAC_PROOF, PROVE, prove, prove_thm.
+
+\ENDDOC
+\DOC{rev\_assoc}
+
+\TYPE {\small\verb%rev_assoc : (* -> (** # *) list -> (** # *))%}\egroup
+
+\SYNOPSIS
+Searches a list of pairs for a pair whose second component equals a specified
+value.
+
+\DESCRIBE
+{\small\verb%rev_assoc y [(x1,y1);...;(xn,yn)]%} returns the first {\small\verb%(xi,yi)%} in the list
+such that {\small\verb%yi%} equals {\small\verb%y%}.
+
+\FAILURE
+Fails if no matching pair is found. This will always be the case if the list
+is empty.
 
-Tactics are produced using the theorem-tactic {\small\verb%ttac%} from all these resolvents
-(failures of {\small\verb%ttac%} at this stage are filtered out) and these tactics are then
-applied in an unspecified sequence to the goal.  That is,
-{\par\samepage\setseps\small
-\begin{verbatim}
-   RES_THEN ttac (A ?- g)
-\end{verbatim}
-}
-\noindent has the effect of:
+\EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-   MAP_EVERY (mapfilter ttac [... ; (ai,aj |- vi) ; ...]) (A ?- g)
+#rev_assoc 2 [(1,4);(3,2);(2,5);(2,6)];;
+(3, 2) : (int # int)
 \end{verbatim}
 }
-\noindent where the theorems {\small\verb%ai,aj |- vi%} are all the consequences that can be
-drawn by a (single) matching modus-ponens inference from the assumptions {\small\verb%A%}
-and the implications derived using {\small\verb%RES_CANON%} from the assumptions.  The
-sequence in which the theorems {\small\verb%ai,aj |- vi%} are generated and the
-corresponding tactics applied is unspecified.
-
-\FAILURE
-Evaluating {\small\verb%RES_THEN ttac th%} fails with `{\small\verb%no implication%}' if no
-implication(s) can be derived from the assumptions of the goal by the
-transformation process described under the entry for {\small\verb%RES_CANON%}.  Evaluating
-{\small\verb%RES_THEN ttac (A ?- g)%} fails with `{\small\verb%no resolvents%}' if no assumption of the
-goal {\small\verb%A ?- g%} can be resolved with the derived implication or implications.
-Evaluation also fails, with `{\small\verb%no tactics%}', if there are resolvents, but for
-every resolvent {\small\verb%ai,aj |- vi%} evaluating the application {\small\verb%ttac (ai,aj |- vi)%}
-fails---that is, if for every resolvent {\small\verb%ttac%} fails to produce a tactic.
-Finally, failure is propagated if any of the tactics that are produced from the
-resolvents by {\small\verb%ttac%} fails when applied in sequence to the goal.
-
 \SEEALSO
-IMP_RES_TAC, IMP_RES_THEN, MATCH_MP, RES_CANON, RES_TAC.
+assoc, find, mem, tryfind, exists, forall.
 
 \ENDDOC
 \DOC{rev}
@@ -21871,33 +21896,6 @@
 
 \ENDDOC
 
-\DOC{rev\_assoc}
-
-\TYPE {\small\verb%rev_assoc : (* -> (** # *) list -> (** # *))%}\egroup
-
-\SYNOPSIS
-Searches a list of pairs for a pair whose second component equals a specified
-value.
-
-\DESCRIBE
-{\small\verb%rev_assoc y [(x1,y1);...;(xn,yn)]%} returns the first {\small\verb%(xi,yi)%} in the list
-such that {\small\verb%yi%} equals {\small\verb%y%}.
-
-\FAILURE
-Fails if no matching pair is found. This will always be the case if the list
-is empty.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#rev_assoc 2 [(1,4);(3,2);(2,5);(2,6)];;
-(3, 2) : (int # int)
-\end{verbatim}
-}
-\SEEALSO
-assoc, find, mem, tryfind, exists, forall.
-
-\ENDDOC
 \DOC{rev\_itlist}
 
 \TYPE {\small\verb%rev_itlist : ((* -> ** -> **) -> * list -> ** -> **)%}\egroup
@@ -21923,185 +21921,72 @@
 itlist, end_itlist.
 
 \ENDDOC
-\DOC{REWRITE\_CONV}
-
-\TYPE {\small\verb%REWRITE_CONV : (thm list -> conv)%}\egroup
-
-\SYNOPSIS
-Rewrites a term including built-in tautologies in the list of rewrites.
-
-\DESCRIBE
-Rewriting a term using {\small\verb%REWRITE_CONV%} utilizes as rewrites two sets
-of theorems: the tautologies in the ML list {\small\verb%basic_rewrites%} and the
-ones supplied by the user. The rule searches top-down and recursively
-for subterms which match the left-hand side of any of the possible
-rewrites, until none of the transformations are applicable. There is no
-ordering specified among the set of rewrites.
-
-Variants of this conversion allow changes in the set of equations used:
-{\small\verb%PURE_REWRITE_CONV%} and others in its family do not rewrite with the
-theorems in {\small\verb%basic_rewrites%}. 
-
-The top-down recursive search for matches may not be desirable, as
-this may increase the number of inferences being made or may result in
-divergence. In this case other rewriting tools such as
-{\small\verb%ONCE_REWRITE_CONV%} and {\small\verb%GEN_REWRITE_CONV%} can be used, or the set of
-theorems given may be reduced.
-
-See {\small\verb%GEN_REWRITE_CONV%} for the general strategy for simplifying
-theorems in HOL using equational theorems.
-
-\FAILURE
-Does not fail, but may diverge if the sequence of rewrites is
-non-terminating.
-
-\USES
-Used to manipulate terms by rewriting them with theorems.
-While resulting in high degree of automation, {\small\verb%REWRITE_CONV%} can
-spawn a large number of inference steps. Thus, variants such
-as {\small\verb%PURE_REWRITE_CONV%}, or other rules such as {\small\verb%SUBST_CONV%}, may be used
-instead to improve efficiency.
-
-\SEEALSO
-basic_rewrites, GEN_REWRITE_CONV, ONCE_REWRITE_CONV,
-PURE_REWRITE_CONV, REWR_CONV, SUBST_CONV.
-
-\ENDDOC
-\DOC{REWRITE\_RULE}
-
-\TYPE {\small\verb%REWRITE_RULE : (thm list -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Rewrites a theorem including built-in tautologies in the list of rewrites.
-
-\DESCRIBE
-Rewriting a theorem using {\small\verb%REWRITE_RULE%} utilizes as rewrites two sets
-of theorems: the tautologies in the ML list {\small\verb%basic_rewrites%} and the
-ones supplied by the user. The rule searches top-down and recursively
-for subterms which match the left-hand side of any of the possible
-rewrites, until none of the transformations are applicable. There is no
-ordering specified among the set of rewrites.
-
-Variants of this rule allow changes in the set of equations used:
-{\small\verb%PURE_REWRITE_RULE%} and others in its family do not rewrite with the
-theorems in {\small\verb%basic_rewrites%}. Rules such as {\small\verb%ASM_REWRITE_RULE%} add the
-assumptions of the object theorem (or a specified subset of these assumptions)
-to the set of possible rewrites.
-
-The top-down recursive search for matches may not be desirable, as
-this may increase the number of inferences being made or may result in
-divergence. In this case other rewriting tools such as
-{\small\verb%ONCE_REWRITE_RULE%} and {\small\verb%GEN_REWRITE_RULE%} can be used, or the set of
-theorems given may be reduced.
-
-See {\small\verb%GEN_REWRITE_RULE%} for the general strategy for simplifying
-theorems in HOL using equational theorems.
-
-\FAILURE
-Does not fail, but may diverge if the sequence of rewrites is
-non-terminating.
-
-\USES
-Used to manipulate theorems by rewriting them with other theorems.
-While resulting in high degree of automation, {\small\verb%REWRITE_RULE%} can
-spawn a large number of inference steps. Thus, variants such
-as {\small\verb%PURE_REWRITE_RULE%}, or other rules such as {\small\verb%SUBST%}, may be used
-instead to improve efficiency.
-
-\SEEALSO
-ASM_REWRITE_RULE, basic_rewrites, GEN_REWRITE_RULE, ONCE_REWRITE_RULE,
-PURE_REWRITE_RULE, REWR_CONV, REWRITE_CONV, SUBST.
-
-\ENDDOC
-\DOC{REWRITE\_TAC}
+\DOC{REW\_DEPTH\_CONV}
 
-\TYPE {\small\verb%REWRITE_TAC : (thm list -> tactic)%}\egroup
+\TYPE {\small\verb%REW_DEPTH_CONV : (conv -> conv)%}\egroup
 
 \SYNOPSIS
-Rewrites a goal including built-in tautologies in the list of rewrites.
+Applies a conversion top-down to all subterms, retraversing changed ones.
+For use in rewriting.
 
 \DESCRIBE
-Rewriting tactics in HOL provide a recursive left-to-right matching
-and rewriting facility that automatically decomposes subgoals and
-justifies segments of proof in which equational theorems are used,
-singly or collectively.  These include the unfolding of definitions,
-and the substitution of equals for equals.  Rewriting is used either
-to advance or to complete the decomposition of subgoals.
-
-{\small\verb%REWRITE_TAC%} transforms (or solves) a goal by using as rewrite rules
-(i.e. as left-to-right replacement rules) the conclusions of the given
-list of (equational) theorems, as well as a set of built-in theorems
-(common tautologies) held in the ML variable {\small\verb%basic_rewrites%}.
-Recognition of a tautology often terminates the subgoaling process
-(i.e. solves the goal).
-
-The equational rewrites generated are applied recursively and to
-arbitrary depth, with matching and instantiation of variables and type
-variables.  A list of rewrites can set off an infinite rewriting
-process, and it is not, of course, decidable in general whether a
-rewrite set has that property. The order in which the rewrite theorems
-are applied is unspecified, and the user should not depend on any
-ordering.
-
-See {\small\verb%GEN_REWRITE_TAC%} for more details on the rewriting process.
-Variants of {\small\verb%REWRITE_TAC%} allow the use of a different set of
-rewrites. Some of them, such as {\small\verb%PURE_REWRITE_TAC%}, exclude the basic
-tautologies from the possible transformations. {\small\verb%ASM_REWRITE_TAC%} and
-others include the assumptions at the goal in the set of possible
-rewrites.
+{\small\verb%REW_DEPTH_CONV c tm%} repeatedly applies the conversion {\small\verb%c%} to all the subterms
+of the term {\small\verb%tm%}, including the term {\small\verb%tm%} itself. The supplied conversion {\small\verb%c%}
+is applied to the subterms of {\small\verb%tm%} in top-down order and is applied repeatedly
+(zero or more times, as is done by {\small\verb%REPEATC%}) at each subterm until it fails.
+If a subterm {\small\verb%t%} is changed (up to alpha-equivalence) by virtue of the
+application of {\small\verb%c%} to its own subterms, then the term into which {\small\verb%t%} is
+transformed is retraversed by applying {\small\verb%REW_DEPTH_CONV c%} to it.
 
-Still other tactics allow greater control over the search for
-rewritable subterms. Several of them such as {\small\verb%ONCE_REWRITE_TAC%} do not
-apply rewrites recursively. {\small\verb%GEN_REWRITE_TAC%} allows a rewrite to be
-applied at a particular subterm.
+{\small\verb%REW_DEPTH_CONV%} is a special version of {\small\verb%TOP_DEPTH_CONV%} for use by the
+rewriting conversions, rules and tactics. It differs from {\small\verb%TOP_DEPTH_CONV%} as
+follows: If converting an abstraction fails due to the presence of the bound
+variable in the hypotheses of the theorem generated by converting the body,
+{\small\verb%REW_DEPTH_CONV%} retries the conversion having renamed the bound variable of
+the abstraction. If successful the renaming is reversed.
 
 \FAILURE
-{\small\verb%REWRITE_TAC%} does not fail. Certain sets of rewriting theorems on
-certain goals may cause a non-terminating sequence of rewrites.
-Divergent rewriting behaviour results from a term {\small\verb%t%} being
-immediately or eventually rewritten to a term containing {\small\verb%t%} as a
-sub-term. The exact behaviour depends on the {\small\verb%HOL%} implementation; it
-may be possible (unfortunately) to fall into Lisp in this event.
+{\small\verb%REW_DEPTH_CONV c tm%} never fails but can diverge.
 
 \EXAMPLE
-The arithmetic theorem {\small\verb%GREATER%}, {\small\verb%|- !m n. m > n = n < m%}, is used
-below to advance a goal:
+The following example illustrates the difference between the functions
+{\small\verb%REW_DEPTH_CONV%} and {\small\verb%TOP_DEPTH_CONV%}. It is not intended to illustrate the
+full range of behaviour of the former. Both {\small\verb%REW_DEPTH_CONV%} and
+{\small\verb%TOP_DEPTH_CONV%} successfully apply the theorem {\small\verb%ADD_0%} inside an abstraction:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #REWRITE_TAC[GREATER]([],"5 > 4");;
-   ([([], "4 < 5")], -) : subgoals
+   #REW_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
+   |- (\n. n + 0) = (\n. n)
+
+   #TOP_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
+   |- (\n. n + 0) = (\n. n)
 \end{verbatim}
 }
-\noindent It is used below with the theorem {\small\verb%LESS_0%},
-{\small\verb%|- !n. 0 < (SUC n)%}, to solve a goal:
+\noindent However, if a hypothesis containing a free occurrence of the bound
+variable is added to the rewrite rule, it interferes with the operation of
+{\small\verb%TOP_DEPTH_CONV%} but not that of {\small\verb%REW_DEPTH_CONV%}:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #let gl,p = REWRITE_TAC[GREATER;LESS_0]([],"(SUC n) > 0");;
-   gl = [] : goal list
-   p = - : proof
+   #let th = ADD_ASSUM "n = 0" ADD_0;;
+   th = n = 0 |- !m. m + 0 = m
+
+   #REW_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
+   n = 0 |- (\n. n + 0) = (\n. n)
 
-   #p[];;
-   |- (SUC n) > 0
+   #TOP_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
+   |- (\n. n + 0) = (\n. n + 0)
 \end{verbatim}
 }
-\USES
-Rewriting is a powerful and general mechanism in HOL, and an
-important part of many proofs.  It relieves the user of the burden of
-directing and justifying a large number of minor proof steps.
-{\small\verb%REWRITE_TAC%} fits a forward proof sequence smoothly into the general
-goal-oriented framework. That is, (within one subgoaling step) it
-produces and justifies certain forward inferences, none of which are
-necessarily on a direct path to the desired goal.
-
-{\small\verb%REWRITE_TAC%} may be more powerful a tactic than is needed in certain
-situations; if efficiency is at stake, alternatives might be
-considered.
+\COMMENTS
+The implementation of this function uses failure to avoid rebuilding
+unchanged subterms. That is to say, during execution the failure string
+{\small\verb%`QCONV`%} may be generated and later trapped. The behaviour of the function
+is dependent on this use of failure. So, if the conversion given as argument
+happens to generate a failure with string {\small\verb%`QCONV`%}, the operation of
+{\small\verb%REW_DEPTH_CONV%} will be unpredictable.
 
 \SEEALSO
-ASM_REWRITE_TAC, GEN_REWRITE_TAC, FILTER_ASM_REWRITE_TAC,
-FILTER_ONCE_ASM_REWRITE_TAC, ONCE_ASM_REWRITE_TAC, ONCE_REWRITE_TAC,
-PURE_ASM_REWRITE_TAC, PURE_ONCE_ASM_REWRITE_TAC,
-PURE_ONCE_REWRITE_TAC, PURE_REWRITE_TAC, REWR_CONV, REWRITE_CONV, SUBST_TAC.
+ONCE_REW_DEPTH_CONV, TOP_DEPTH_CONV.
 
 \ENDDOC
 \DOC{REWR\_CONV}
@@ -22271,72 +22156,185 @@
 REWRITE_CONV.
 
 \ENDDOC
-\DOC{REW\_DEPTH\_CONV}
+\DOC{REWRITE\_CONV}
 
-\TYPE {\small\verb%REW_DEPTH_CONV : (conv -> conv)%}\egroup
+\TYPE {\small\verb%REWRITE_CONV : (thm list -> conv)%}\egroup
 
 \SYNOPSIS
-Applies a conversion top-down to all subterms, retraversing changed ones.
-For use in rewriting.
+Rewrites a term including built-in tautologies in the list of rewrites.
 
 \DESCRIBE
-{\small\verb%REW_DEPTH_CONV c tm%} repeatedly applies the conversion {\small\verb%c%} to all the subterms
-of the term {\small\verb%tm%}, including the term {\small\verb%tm%} itself. The supplied conversion {\small\verb%c%}
-is applied to the subterms of {\small\verb%tm%} in top-down order and is applied repeatedly
-(zero or more times, as is done by {\small\verb%REPEATC%}) at each subterm until it fails.
-If a subterm {\small\verb%t%} is changed (up to alpha-equivalence) by virtue of the
-application of {\small\verb%c%} to its own subterms, then the term into which {\small\verb%t%} is
-transformed is retraversed by applying {\small\verb%REW_DEPTH_CONV c%} to it.
+Rewriting a term using {\small\verb%REWRITE_CONV%} utilizes as rewrites two sets
+of theorems: the tautologies in the ML list {\small\verb%basic_rewrites%} and the
+ones supplied by the user. The rule searches top-down and recursively
+for subterms which match the left-hand side of any of the possible
+rewrites, until none of the transformations are applicable. There is no
+ordering specified among the set of rewrites.
 
-{\small\verb%REW_DEPTH_CONV%} is a special version of {\small\verb%TOP_DEPTH_CONV%} for use by the
-rewriting conversions, rules and tactics. It differs from {\small\verb%TOP_DEPTH_CONV%} as
-follows: If converting an abstraction fails due to the presence of the bound
-variable in the hypotheses of the theorem generated by converting the body,
-{\small\verb%REW_DEPTH_CONV%} retries the conversion having renamed the bound variable of
-the abstraction. If successful the renaming is reversed.
+Variants of this conversion allow changes in the set of equations used:
+{\small\verb%PURE_REWRITE_CONV%} and others in its family do not rewrite with the
+theorems in {\small\verb%basic_rewrites%}. 
+
+The top-down recursive search for matches may not be desirable, as
+this may increase the number of inferences being made or may result in
+divergence. In this case other rewriting tools such as
+{\small\verb%ONCE_REWRITE_CONV%} and {\small\verb%GEN_REWRITE_CONV%} can be used, or the set of
+theorems given may be reduced.
+
+See {\small\verb%GEN_REWRITE_CONV%} for the general strategy for simplifying
+theorems in HOL using equational theorems.
 
 \FAILURE
-{\small\verb%REW_DEPTH_CONV c tm%} never fails but can diverge.
+Does not fail, but may diverge if the sequence of rewrites is
+non-terminating.
+
+\USES
+Used to manipulate terms by rewriting them with theorems.
+While resulting in high degree of automation, {\small\verb%REWRITE_CONV%} can
+spawn a large number of inference steps. Thus, variants such
+as {\small\verb%PURE_REWRITE_CONV%}, or other rules such as {\small\verb%SUBST_CONV%}, may be used
+instead to improve efficiency.
+
+\SEEALSO
+basic_rewrites, GEN_REWRITE_CONV, ONCE_REWRITE_CONV,
+PURE_REWRITE_CONV, REWR_CONV, SUBST_CONV.
+
+\ENDDOC
+\DOC{REWRITE\_RULE}
+
+\TYPE {\small\verb%REWRITE_RULE : (thm list -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Rewrites a theorem including built-in tautologies in the list of rewrites.
+
+\DESCRIBE
+Rewriting a theorem using {\small\verb%REWRITE_RULE%} utilizes as rewrites two sets
+of theorems: the tautologies in the ML list {\small\verb%basic_rewrites%} and the
+ones supplied by the user. The rule searches top-down and recursively
+for subterms which match the left-hand side of any of the possible
+rewrites, until none of the transformations are applicable. There is no
+ordering specified among the set of rewrites.
+
+Variants of this rule allow changes in the set of equations used:
+{\small\verb%PURE_REWRITE_RULE%} and others in its family do not rewrite with the
+theorems in {\small\verb%basic_rewrites%}. Rules such as {\small\verb%ASM_REWRITE_RULE%} add the
+assumptions of the object theorem (or a specified subset of these assumptions)
+to the set of possible rewrites.
+
+The top-down recursive search for matches may not be desirable, as
+this may increase the number of inferences being made or may result in
+divergence. In this case other rewriting tools such as
+{\small\verb%ONCE_REWRITE_RULE%} and {\small\verb%GEN_REWRITE_RULE%} can be used, or the set of
+theorems given may be reduced.
+
+See {\small\verb%GEN_REWRITE_RULE%} for the general strategy for simplifying
+theorems in HOL using equational theorems.
+
+\FAILURE
+Does not fail, but may diverge if the sequence of rewrites is
+non-terminating.
+
+\USES
+Used to manipulate theorems by rewriting them with other theorems.
+While resulting in high degree of automation, {\small\verb%REWRITE_RULE%} can
+spawn a large number of inference steps. Thus, variants such
+as {\small\verb%PURE_REWRITE_RULE%}, or other rules such as {\small\verb%SUBST%}, may be used
+instead to improve efficiency.
+
+\SEEALSO
+ASM_REWRITE_RULE, basic_rewrites, GEN_REWRITE_RULE, ONCE_REWRITE_RULE,
+PURE_REWRITE_RULE, REWR_CONV, REWRITE_CONV, SUBST.
+
+\ENDDOC
+\DOC{REWRITE\_TAC}
+
+\TYPE {\small\verb%REWRITE_TAC : (thm list -> tactic)%}\egroup
+
+\SYNOPSIS
+Rewrites a goal including built-in tautologies in the list of rewrites.
+
+\DESCRIBE
+Rewriting tactics in HOL provide a recursive left-to-right matching
+and rewriting facility that automatically decomposes subgoals and
+justifies segments of proof in which equational theorems are used,
+singly or collectively.  These include the unfolding of definitions,
+and the substitution of equals for equals.  Rewriting is used either
+to advance or to complete the decomposition of subgoals.
+
+{\small\verb%REWRITE_TAC%} transforms (or solves) a goal by using as rewrite rules
+(i.e. as left-to-right replacement rules) the conclusions of the given
+list of (equational) theorems, as well as a set of built-in theorems
+(common tautologies) held in the ML variable {\small\verb%basic_rewrites%}.
+Recognition of a tautology often terminates the subgoaling process
+(i.e. solves the goal).
+
+The equational rewrites generated are applied recursively and to
+arbitrary depth, with matching and instantiation of variables and type
+variables.  A list of rewrites can set off an infinite rewriting
+process, and it is not, of course, decidable in general whether a
+rewrite set has that property. The order in which the rewrite theorems
+are applied is unspecified, and the user should not depend on any
+ordering.
+
+See {\small\verb%GEN_REWRITE_TAC%} for more details on the rewriting process.
+Variants of {\small\verb%REWRITE_TAC%} allow the use of a different set of
+rewrites. Some of them, such as {\small\verb%PURE_REWRITE_TAC%}, exclude the basic
+tautologies from the possible transformations. {\small\verb%ASM_REWRITE_TAC%} and
+others include the assumptions at the goal in the set of possible
+rewrites.
+
+Still other tactics allow greater control over the search for
+rewritable subterms. Several of them such as {\small\verb%ONCE_REWRITE_TAC%} do not
+apply rewrites recursively. {\small\verb%GEN_REWRITE_TAC%} allows a rewrite to be
+applied at a particular subterm.
+
+\FAILURE
+{\small\verb%REWRITE_TAC%} does not fail. Certain sets of rewriting theorems on
+certain goals may cause a non-terminating sequence of rewrites.
+Divergent rewriting behaviour results from a term {\small\verb%t%} being
+immediately or eventually rewritten to a term containing {\small\verb%t%} as a
+sub-term. The exact behaviour depends on the {\small\verb%HOL%} implementation; it
+may be possible (unfortunately) to fall into Lisp in this event.
 
 \EXAMPLE
-The following example illustrates the difference between the functions
-{\small\verb%REW_DEPTH_CONV%} and {\small\verb%TOP_DEPTH_CONV%}. It is not intended to illustrate the
-full range of behaviour of the former. Both {\small\verb%REW_DEPTH_CONV%} and
-{\small\verb%TOP_DEPTH_CONV%} successfully apply the theorem {\small\verb%ADD_0%} inside an abstraction:
+The arithmetic theorem {\small\verb%GREATER%}, {\small\verb%|- !m n. m > n = n < m%}, is used
+below to advance a goal:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #REW_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
-   |- (\n. n + 0) = (\n. n)
-
-   #TOP_DEPTH_CONV (REWR_CONV ADD_0) "\n. n + 0";;
-   |- (\n. n + 0) = (\n. n)
+   #REWRITE_TAC[GREATER]([],"5 > 4");;
+   ([([], "4 < 5")], -) : subgoals
 \end{verbatim}
 }
-\noindent However, if a hypothesis containing a free occurrence of the bound
-variable is added to the rewrite rule, it interferes with the operation of
-{\small\verb%TOP_DEPTH_CONV%} but not that of {\small\verb%REW_DEPTH_CONV%}:
+\noindent It is used below with the theorem {\small\verb%LESS_0%},
+{\small\verb%|- !n. 0 < (SUC n)%}, to solve a goal:
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #let th = ADD_ASSUM "n = 0" ADD_0;;
-   th = n = 0 |- !m. m + 0 = m
-
-   #REW_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
-   n = 0 |- (\n. n + 0) = (\n. n)
+   #let gl,p = REWRITE_TAC[GREATER;LESS_0]([],"(SUC n) > 0");;
+   gl = [] : goal list
+   p = - : proof
 
-   #TOP_DEPTH_CONV (REWR_CONV th) "\n. n + 0";;
-   |- (\n. n + 0) = (\n. n + 0)
+   #p[];;
+   |- (SUC n) > 0
 \end{verbatim}
 }
-\COMMENTS
-The implementation of this function uses failure to avoid rebuilding
-unchanged subterms. That is to say, during execution the failure string
-{\small\verb%`QCONV`%} may be generated and later trapped. The behaviour of the function
-is dependent on this use of failure. So, if the conversion given as argument
-happens to generate a failure with string {\small\verb%`QCONV`%}, the operation of
-{\small\verb%REW_DEPTH_CONV%} will be unpredictable.
+\USES
+Rewriting is a powerful and general mechanism in HOL, and an
+important part of many proofs.  It relieves the user of the burden of
+directing and justifying a large number of minor proof steps.
+{\small\verb%REWRITE_TAC%} fits a forward proof sequence smoothly into the general
+goal-oriented framework. That is, (within one subgoaling step) it
+produces and justifies certain forward inferences, none of which are
+necessarily on a direct path to the desired goal.
+
+{\small\verb%REWRITE_TAC%} may be more powerful a tactic than is needed in certain
+situations; if efficiency is at stake, alternatives might be
+considered.
 
 \SEEALSO
-ONCE_REW_DEPTH_CONV, TOP_DEPTH_CONV.
+ASM_REWRITE_TAC, GEN_REWRITE_TAC, FILTER_ASM_REWRITE_TAC,
+FILTER_ONCE_ASM_REWRITE_TAC, ONCE_ASM_REWRITE_TAC, ONCE_REWRITE_TAC,
+PURE_ASM_REWRITE_TAC, PURE_ONCE_ASM_REWRITE_TAC,
+PURE_ONCE_REWRITE_TAC, PURE_REWRITE_TAC, REWR_CONV, REWRITE_CONV, SUBST_TAC.
 
 \ENDDOC
 \DOC{rhs}
@@ -22722,20 +22720,6 @@
 ASSUM_LIST, MAP_EVERY, MAP_FIRST, POP_ASSUM_LIST.
 
 \ENDDOC
-\DOC{S}
-
-\TYPE {\small\verb%S : ((* -> ** -> ***) -> (* -> **) -> * -> ***)%}\egroup
-
-\SYNOPSIS
-Performs function composition: {\small\verb%S f g x%} = {\small\verb%f x (g x)%} (the {\small\verb%S%} combinator).
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-\#, B, C, CB, Co, I, K, KI, o, oo, W.
-
-\ENDDOC
 \DOC{save}
 
 \TYPE {\small\verb%save : (string -> void)%}\egroup
@@ -22977,10 +22961,24 @@
 }
 
 \SEEALSO
-SCANL_CONV, FOLDL_CONV, FOLDR_CONV, list_FOLD_CONV.
+SCANL_CONV, FOLDL_CONV, FOLDR_CONV, list_FOLD_CONV.
+
+\ENDDOC
+
+\DOC{S}
+
+\TYPE {\small\verb%S : ((* -> ** -> ***) -> (* -> **) -> * -> ***)%}\egroup
+
+\SYNOPSIS
+Performs function composition: {\small\verb%S f g x%} = {\small\verb%f x (g x)%} (the {\small\verb%S%} combinator).
+
+\FAILURE
+Never fails.
+
+\SEEALSO
+\#, B, C, CB, Co, I, K, KI, o, oo, W.
 
 \ENDDOC
-
 \DOC{search\_path}
 
 \TYPE {\small\verb%search_path : (void -> string list)%}\egroup
@@ -23327,35 +23325,6 @@
 CHOOSE, SELECT_AX, SELECT_CONV, SELECT_ELIM, SELECT_INTRO.
 
 \ENDDOC
-\DOC{setify}
-
-\TYPE {\small\verb%setify : (* list -> * list)%}\egroup
-
-\SYNOPSIS
-Removes repeated elements from a list. Makes a list into a `set'.
-
-\DESCRIBE
-{\small\verb%setify l%} removes repeated elements from {\small\verb%l%}, leaving the last occurrence of
-each duplicate in the list.
-
-\FAILURE
-Never fails.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#setify [1;2;3;1;4;3];;
-[2; 1; 4; 3] : int list
-\end{verbatim}
-}
-\COMMENTS
-Perhaps the first occurrence of each duplicate should be left in the list, not
-the last? However, other functions may rely on the ordering currently used.
-
-\SEEALSO
-distinct.
-
-\ENDDOC
 \DOC{set\_equal}
 
 \TYPE {\small\verb%set_equal : (* list -> * list -> bool)%}\egroup
@@ -23599,6 +23568,35 @@
 help_search_path, install, search_path, set_search_path.
 
 \ENDDOC
+\DOC{setify}
+
+\TYPE {\small\verb%setify : (* list -> * list)%}\egroup
+
+\SYNOPSIS
+Removes repeated elements from a list. Makes a list into a `set'.
+
+\DESCRIBE
+{\small\verb%setify l%} removes repeated elements from {\small\verb%l%}, leaving the last occurrence of
+each duplicate in the list.
+
+\FAILURE
+Never fails.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#setify [1;2;3;1;4;3];;
+[2; 1; 4; 3] : int list
+\end{verbatim}
+}
+\COMMENTS
+Perhaps the first occurrence of each duplicate should be left in the list, not
+the last? However, other functions may rely on the ordering currently used.
+
+\SEEALSO
+distinct.
+
+\ENDDOC
 \DOC{set\_interface\_map}
 
 \TYPE {\small\verb%set_interface_map : ((string # string) list -> (string # string) list)%}\egroup
@@ -24272,6 +24270,45 @@
 \end{verbatim}
 }
 \ENDDOC
+\DOC{SPEC\_ALL}
+
+\TYPE {\small\verb%SPEC_ALL : (thm -> thm)%}\egroup
+
+\SYNOPSIS
+Specializes the conclusion of a theorem with its own quantified variables.
+
+\DESCRIBE
+When applied to a theorem {\small\verb%A |- !x1...xn. t%}, the inference rule {\small\verb%SPEC_ALL%}
+returns the theorem {\small\verb%A |- t[x1'/x1]...[xn'/xn]%} where the {\small\verb%xi'%} are distinct
+variants of the corresponding {\small\verb%xi%}, chosen to avoid clashes with any variables
+free in the assumption list and with the names of constants. Normally {\small\verb%xi'%} is
+just {\small\verb%xi%}, in which case {\small\verb%SPEC_ALL%} simply removes all universal quantifiers.
+{\par\samepage\setseps\small
+\begin{verbatim}
+       A |- !x1...xn. t
+   ---------------------------  SPEC_ALL
+    A |- t[x1'/x1]...[xn'/xn]
+\end{verbatim}
+}
+\FAILURE
+Never fails.
+
+\EXAMPLE
+The following example shows how variables are also renamed to avoid clashing
+with the names of constants.
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #let v=mk_var(`T`,":bool") in ASSUME "!^v. ^v \/ ~^v";;
+   !T. T \/ ~T |- !T. T \/ ~T
+
+   #SPEC_ALL it;;
+   !T. T \/ ~T |- T' \/ ~T'
+\end{verbatim}
+}
+\SEEALSO
+GEN, GENL, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
+
+\ENDDOC
 \DOC{SPEC}
 
 \TYPE {\small\verb%SPEC : (term -> thm -> thm)%}\egroup
@@ -24379,45 +24416,6 @@
 GEN, GENL, GEN_ALL, GEN_TAC, SPEC, SPEC_ALL, SPEC_TAC.
 
 \ENDDOC
-\DOC{SPEC\_ALL}
-
-\TYPE {\small\verb%SPEC_ALL : (thm -> thm)%}\egroup
-
-\SYNOPSIS
-Specializes the conclusion of a theorem with its own quantified variables.
-
-\DESCRIBE
-When applied to a theorem {\small\verb%A |- !x1...xn. t%}, the inference rule {\small\verb%SPEC_ALL%}
-returns the theorem {\small\verb%A |- t[x1'/x1]...[xn'/xn]%} where the {\small\verb%xi'%} are distinct
-variants of the corresponding {\small\verb%xi%}, chosen to avoid clashes with any variables
-free in the assumption list and with the names of constants. Normally {\small\verb%xi'%} is
-just {\small\verb%xi%}, in which case {\small\verb%SPEC_ALL%} simply removes all universal quantifiers.
-{\par\samepage\setseps\small
-\begin{verbatim}
-       A |- !x1...xn. t
-   ---------------------------  SPEC_ALL
-    A |- t[x1'/x1]...[xn'/xn]
-\end{verbatim}
-}
-\FAILURE
-Never fails.
-
-\EXAMPLE
-The following example shows how variables are also renamed to avoid clashing
-with the names of constants.
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #let v=mk_var(`T`,":bool") in ASSUME "!^v. ^v \/ ~^v";;
-   !T. T \/ ~T |- !T. T \/ ~T
-
-   #SPEC_ALL it;;
-   !T. T \/ ~T |- T' \/ ~T'
-\end{verbatim}
-}
-\SEEALSO
-GEN, GENL, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
-
-\ENDDOC
 \DOC{SPEC\_TAC}
 
 \TYPE {\small\verb%SPEC_TAC : ((term # term) -> tactic)%}\egroup
@@ -25123,6 +25121,50 @@
 ASM_CASES_TAC, BOOL_CASES_TAC, COND_CASES_TAC, DISJ_CASES_TAC.
 
 \ENDDOC
+\DOC{SUB\_CONV}
+
+\TYPE {\small\verb%SUB_CONV : (conv -> conv)%}\egroup
+
+\SYNOPSIS
+Applies a conversion to the top-level subterms of a term.
+
+\DESCRIBE
+For any conversion {\small\verb%c%}, the function returned by {\small\verb%SUB_CONV c%} is a conversion
+that applies {\small\verb%c%} to all the top-level subterms of a term.  If the conversion
+{\small\verb%c%} maps {\small\verb%t%} to {\small\verb%|- t = t'%}, then {\small\verb%SUB_CONV c%} maps an abstraction {\small\verb%"\x.t"%} to
+the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- (\x.t) = (\x.t')
+\end{verbatim}
+}
+\noindent That is, {\small\verb%SUB_CONV c "\x.t"%} applies {\small\verb%c%} to the body of the
+abstraction {\small\verb%"\x.t"%}.  If {\small\verb%c%} is a conversion that maps {\small\verb%"t1"%} to the theorem
+{\small\verb%|- t1 = t1'%} and {\small\verb%"t2"%} to the theorem {\small\verb%|- t2 = t2'%}, then the conversion
+{\small\verb%SUB_CONV c%} maps an application {\small\verb%"t1 t2"%} to the theorem:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   |- (t1 t2) = (t1' t2')
+\end{verbatim}
+}
+\noindent That is, {\small\verb%SUB_CONV c "t1 t2"%} applies {\small\verb%c%} to the both the operator
+{\small\verb%t1%} and the operand {\small\verb%t2%} of the application {\small\verb%"t1 t2"%}.  Finally, for any
+conversion {\small\verb%c%}, the function returned by {\small\verb%SUB_CONV c%} acts as the identity
+conversion on variables and constants.  That is, if {\small\verb%"t"%} is a variable or
+constant, then {\small\verb%SUB_CONV c "t"%} returns {\small\verb%|- t = t%}.
+
+\FAILURE
+{\small\verb%SUB_CONV c tm%} fails if {\small\verb%tm%} is an abstraction {\small\verb%"\x.t"%} and the conversion {\small\verb%c%}
+fails when applied to {\small\verb%t%}, or if {\small\verb%tm%} is an application {\small\verb%"t1 t2"%} and the
+conversion {\small\verb%c%} fails when applied to either {\small\verb%t1%} or {\small\verb%t2%}.  The function
+returned by {\small\verb%SUB_CONV c%} may also fail if the ML function {\small\verb%c:term->thm%} is not,
+in fact, a conversion (i.e. a function that maps a term {\small\verb%t%} to a theorem
+{\small\verb%|- t = t'%}).
+
+\SEEALSO
+ABS_CONV, RAND_CONV, RATOR_CONV.
+
+\ENDDOC
 \DOC{SUBGOAL\_THEN}
 
 \TYPE {\small\verb%SUBGOAL_THEN : (term -> thm_tactic -> tactic)%}\egroup
@@ -25220,141 +25262,80 @@
 \begin{verbatim}
    #let thm1 = SPECL ["m:num"; "n:num"] ADD_SYM
    #and thm2 = CONJUNCT1 ADD_CLAUSES;;
-   thm1 = |- m + n = n + m
-   thm2 = |- 0 + m = m
-\end{verbatim}
-}
-\noindent depending on the occurrence of free subterms
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #SUBS [thm1; thm2] (ASSUME "(n + 0) + (0 + m) = m + n");;
-   . |- (n + 0) + m = n + m
-
-   #SUBS [thm1; thm2] (ASSUME "!n. (n + 0) + (0 + m) = m + n");;
-   . |- !n. (n + 0) + m = m + n
-\end{verbatim}
-}
-\USES
-{\small\verb%SUBS%} can sometimes be used when rewriting (for example, with {\small\verb%REWRITE_RULE%})
-would diverge and term instantiation is not needed.  Moreover, applying the
-substitution rules is often much faster than using the rewriting rules.
-
-\SEEALSO
-ONCE_REWRITE_RULE, PURE_REWRITE_RULE, REWRITE_RULE, SUBST, SUBST_MATCH,
-SUBS_OCCS.
-
-\ENDDOC
-\DOC{SUBST}
-
-\TYPE {\small\verb%SUBST : ((thm # term) list -> term -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Makes a set of parallel substitutions in a theorem.
-
-\DESCRIBE
-Implements the following rule of simultaneous substitution
-{\par\samepage\setseps\small
-\begin{verbatim}
-    A1 |- t1 = u1 ,  ... , An |- tn = un ,    A |- t[t1,...,tn]
-   -------------------------------------------------------------
-                  A u A1 u ... u An |- t[ui]
-\end{verbatim}
-}
-\noindent Evaluating
-{\par\samepage\setseps\small
-\begin{verbatim}
-   SUBST [((A1 |- t1=u1), x1); ... ;((An |- tn=un), xn)]
-         t[x1,...,xn]
-         (A |- t[t1,...,tn])
-\end{verbatim}
-}
-\noindent returns the theorem {\small\verb%A |- t[u1,...,un]%}.  The term argument
-{\small\verb%t[x1,...,xn]%} is a template which should match the conclusion of the theorem
-being substituted into, with the variables {\small\verb%x1%}, ... , {\small\verb%xn%} marking those
-places where occurrences of {\small\verb%t1%}, ... , {\small\verb%tn%} are to be replaced by the terms
-{\small\verb%u1%}, ... , {\small\verb%un%}, respectively.  The occurrence of {\small\verb%ti%} at the places marked by
-{\small\verb%xi%} must be free (i.e. {\small\verb%ti%} must not contain any bound variables).  {\small\verb%SUBST%}
-automatically renames bound variables to prevent free variables in {\small\verb%ui%}
-becoming bound after substitution.
-
-{\small\verb%SUBST%} is a complex primitive because it performs both parallel simultaneous
-substitution and renaming of variables. This is for efficiency reasons, but it
-would be logically cleaner if {\small\verb%SUBST%} were simpler.
-
-\FAILURE
-If the template does not match the conclusion of the hypothesis, or the terms
-in the conclusion marked by the variables {\small\verb%x1%}, ... , {\small\verb%xn%} in the template are
-not identical to the left hand sides of the supplied equations (i.e. the terms
-{\small\verb%t1%}, ... , {\small\verb%tn%}).
-
-\EXAMPLE
+   thm1 = |- m + n = n + m
+   thm2 = |- 0 + m = m
+\end{verbatim}
+}
+\noindent depending on the occurrence of free subterms
 {\par\samepage\setseps\small
 \begin{verbatim}
-#let th0 = SPEC "0" ADD1 and th1 = SPEC "1" ADD1;;
-th0 = |- SUC 0 = 0 + 1
-th1 = |- SUC 1 = 1 + 1
-
-#SUBST [(th0,"x:num");(th1,"y:num")]
-#      "(x+y) > SUC 0"
-#      (ASSUME "(SUC 0 + SUC 1) > SUC 0");;
-. |- ((0 + 1) + (1 + 1)) > (SUC 0)
-
-#SUBST [(th0,"x:num");(th1,"y:num")]
-#      "(SUC 0 + y) > SUC 0"
-#      (ASSUME "(SUC 0 + SUC 1) > SUC 0");;
-. |- ((SUC 0) + (1 + 1)) > (SUC 0)
+   #SUBS [thm1; thm2] (ASSUME "(n + 0) + (0 + m) = m + n");;
+   . |- (n + 0) + m = n + m
 
-#SUBST [(th0,"x:num");(th1,"y:num")]
-#      "(x+y) > x"
-#      (ASSUME "(SUC 0 + SUC 1) > SUC 0");;
-. |- ((0 + 1) + (1 + 1)) > (0 + 1)
+   #SUBS [thm1; thm2] (ASSUME "!n. (n + 0) + (0 + m) = m + n");;
+   . |- !n. (n + 0) + m = m + n
 \end{verbatim}
 }
 \USES
-For substituting at selected occurrences. Often useful
-for writing special purpose derived inference rules.
+{\small\verb%SUBS%} can sometimes be used when rewriting (for example, with {\small\verb%REWRITE_RULE%})
+would diverge and term instantiation is not needed.  Moreover, applying the
+substitution rules is often much faster than using the rewriting rules.
 
 \SEEALSO
-SUBS.
+ONCE_REWRITE_RULE, PURE_REWRITE_RULE, REWRITE_RULE, SUBST, SUBST_MATCH,
+SUBS_OCCS.
 
 \ENDDOC
-\DOC{subst}
+\DOC{SUBS\_OCCS}
 
-\TYPE {\small\verb%subst : ((term # term) list -> term -> term)%}\egroup
+\TYPE {\small\verb%SUBS_OCCS : ((int list # thm) list -> thm -> thm)%}\egroup
 
 \SYNOPSIS
-Substitutes terms in a term.
+Makes substitutions in a theorem at specific occurrences of a term, using a
+list of equational theorems.
 
 \DESCRIBE
-Given a list of term pairs {\small\verb%[("a_1","b_1"),...,("a_n","b_n")]%}
-and a term {\small\verb%"c"%}, {\small\verb%subst%} attempts to substitute  all free occurrences of
-{\small\verb%"b_i"%} in {\small\verb%"c"%} by {\small\verb%"a_i"%} for all {\small\verb%i%} ranging between {\small\verb%1%} and {\small\verb%n%}.
-
+Given a list {\small\verb%(l1,A1|-t1=v1),...,(ln,An|-tn=vn)%} and a theorem
+{\small\verb%(A|-t)%}, {\small\verb%SUBS_OCCS%} simultaneously replaces each {\small\verb%ti%} in {\small\verb%t%} with {\small\verb%vi%},
+at the occurrences specified by the integers
+in the list {\small\verb%li = [o1;...;ok]%} for each theorem {\small\verb%Ai|-ti=vi%}.
+{\par\samepage\setseps\small
+\begin{verbatim}
+     (l1,A1|-t1=v1) ... (ln,An|-tn=vn)  A|-t
+   -------------------------------------------  SUBS_OCCS[(l1,A1|-t1=v1);...;
+    A1 u ... An u A |- t[v1,...,vn/t1,...,tn]            (ln,An|-tn=vn)] (A|-t)
+\end{verbatim}
+}
 \FAILURE
-Failure occurs if for some {\small\verb%i%} ranging between {\small\verb%1%} and {\small\verb%n%}, the substitution
-of {\small\verb%"b_i"%} by {\small\verb%"a_i"%} fails.
-The substitution of  {\small\verb%"b_i"%} by {\small\verb%"a_i"%} fails for some {\small\verb%i%},
-if the types of {\small\verb%"a_i"%} and  {\small\verb%"b_i"%} are not the same.
+{\small\verb%SUBS_OCCS [(l1,th1);...;(ln,thn)] (A|-t)%} fails if
+the conclusion of any theorem in the list is not an equation.
+No change is made to the theorem if the supplied occurrences {\small\verb%li%} of the
+left-hand side of the conclusion of {\small\verb%thi%} do not appear in {\small\verb%t%}.
 
 \EXAMPLE
+The commutative law for addition
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #subst [("1","SUC 0")] "SUC(SUC 0)";;
-   "SUC 1" : term
-
-   #subst [("1","SUC 0");("2","SUC 1")] "SUC(SUC 0)";;
-   "SUC 1" : term
-
-   #subst [("1","SUC 0");("2","SUC 1")] "SUC(SUC 0) = SUC 1";;
-   "SUC 1 = 2" : term
-
-   #subst [("b:num","a:num")] "\a:num. (b:num)";;
-   "\a. b" : term
-
-   #subst [("foo:*","flip:*")] "waddle:*";;
-   "waddle" : term
+   #let thm = SPECL ["m:num"; "n:num"] ADD_SYM;;
+   thm = |- m + n = n + m
+\end{verbatim}
+}
+\noindent can be used for substituting only the second occurrence of
+the subterm {\small\verb%m + n%}
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #SUBS_OCCS [([2],thm)] (ASSUME "(n + m) + (m + n) = (m + n) + (m + n)");;
+   . |- (n + m) + (m + n) = (n + m) + (m + n)
 \end{verbatim}
 }
+\USES
+{\small\verb%SUBS_OCCS%} is used when rewriting at specific occurrences of a term, and rules
+such as {\small\verb%REWRITE_RULE%}, {\small\verb%PURE_REWRITE_RULE%}, {\small\verb%ONCE_REWRITE_RULE%}, and {\small\verb%SUBS%}
+are too extensive or would diverge.
+
+\SEEALSO
+ONCE_REWRITE_RULE, PURE_REWRITE_RULE, REWRITE_RULE, SUBS, SUBST, SUBST_MATCH.
+
 \ENDDOC
 \DOC{SUBST1\_TAC}
 
@@ -25549,6 +25530,118 @@
 REWR_CONV, SUBS, SUBST, SUBS_OCCS.
 
 \ENDDOC
+\DOC{subst}
+
+\TYPE {\small\verb%subst : ((term # term) list -> term -> term)%}\egroup
+
+\SYNOPSIS
+Substitutes terms in a term.
+
+\DESCRIBE
+Given a list of term pairs {\small\verb%[("a_1","b_1"),...,("a_n","b_n")]%}
+and a term {\small\verb%"c"%}, {\small\verb%subst%} attempts to substitute  all free occurrences of
+{\small\verb%"b_i"%} in {\small\verb%"c"%} by {\small\verb%"a_i"%} for all {\small\verb%i%} ranging between {\small\verb%1%} and {\small\verb%n%}.
+
+\FAILURE
+Failure occurs if for some {\small\verb%i%} ranging between {\small\verb%1%} and {\small\verb%n%}, the substitution
+of {\small\verb%"b_i"%} by {\small\verb%"a_i"%} fails.
+The substitution of  {\small\verb%"b_i"%} by {\small\verb%"a_i"%} fails for some {\small\verb%i%},
+if the types of {\small\verb%"a_i"%} and  {\small\verb%"b_i"%} are not the same.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #subst [("1","SUC 0")] "SUC(SUC 0)";;
+   "SUC 1" : term
+
+   #subst [("1","SUC 0");("2","SUC 1")] "SUC(SUC 0)";;
+   "SUC 1" : term
+
+   #subst [("1","SUC 0");("2","SUC 1")] "SUC(SUC 0) = SUC 1";;
+   "SUC 1 = 2" : term
+
+   #subst [("b:num","a:num")] "\a:num. (b:num)";;
+   "\a. b" : term
+
+   #subst [("foo:*","flip:*")] "waddle:*";;
+   "waddle" : term
+\end{verbatim}
+}
+\ENDDOC
+\DOC{SUBST}
+
+\TYPE {\small\verb%SUBST : ((thm # term) list -> term -> thm -> thm)%}\egroup
+
+\SYNOPSIS
+Makes a set of parallel substitutions in a theorem.
+
+\DESCRIBE
+Implements the following rule of simultaneous substitution
+{\par\samepage\setseps\small
+\begin{verbatim}
+    A1 |- t1 = u1 ,  ... , An |- tn = un ,    A |- t[t1,...,tn]
+   -------------------------------------------------------------
+                  A u A1 u ... u An |- t[ui]
+\end{verbatim}
+}
+\noindent Evaluating
+{\par\samepage\setseps\small
+\begin{verbatim}
+   SUBST [((A1 |- t1=u1), x1); ... ;((An |- tn=un), xn)]
+         t[x1,...,xn]
+         (A |- t[t1,...,tn])
+\end{verbatim}
+}
+\noindent returns the theorem {\small\verb%A |- t[u1,...,un]%}.  The term argument
+{\small\verb%t[x1,...,xn]%} is a template which should match the conclusion of the theorem
+being substituted into, with the variables {\small\verb%x1%}, ... , {\small\verb%xn%} marking those
+places where occurrences of {\small\verb%t1%}, ... , {\small\verb%tn%} are to be replaced by the terms
+{\small\verb%u1%}, ... , {\small\verb%un%}, respectively.  The occurrence of {\small\verb%ti%} at the places marked by
+{\small\verb%xi%} must be free (i.e. {\small\verb%ti%} must not contain any bound variables).  {\small\verb%SUBST%}
+automatically renames bound variables to prevent free variables in {\small\verb%ui%}
+becoming bound after substitution.
+
+{\small\verb%SUBST%} is a complex primitive because it performs both parallel simultaneous
+substitution and renaming of variables. This is for efficiency reasons, but it
+would be logically cleaner if {\small\verb%SUBST%} were simpler.
+
+\FAILURE
+If the template does not match the conclusion of the hypothesis, or the terms
+in the conclusion marked by the variables {\small\verb%x1%}, ... , {\small\verb%xn%} in the template are
+not identical to the left hand sides of the supplied equations (i.e. the terms
+{\small\verb%t1%}, ... , {\small\verb%tn%}).
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#let th0 = SPEC "0" ADD1 and th1 = SPEC "1" ADD1;;
+th0 = |- SUC 0 = 0 + 1
+th1 = |- SUC 1 = 1 + 1
+
+#SUBST [(th0,"x:num");(th1,"y:num")]
+#      "(x+y) > SUC 0"
+#      (ASSUME "(SUC 0 + SUC 1) > SUC 0");;
+. |- ((0 + 1) + (1 + 1)) > (SUC 0)
+
+#SUBST [(th0,"x:num");(th1,"y:num")]
+#      "(SUC 0 + y) > SUC 0"
+#      (ASSUME "(SUC 0 + SUC 1) > SUC 0");;
+. |- ((SUC 0) + (1 + 1)) > (SUC 0)
+
+#SUBST [(th0,"x:num");(th1,"y:num")]
+#      "(x+y) > x"
+#      (ASSUME "(SUC 0 + SUC 1) > SUC 0");;
+. |- ((0 + 1) + (1 + 1)) > (0 + 1)
+\end{verbatim}
+}
+\USES
+For substituting at selected occurrences. Often useful
+for writing special purpose derived inference rules.
+
+\SEEALSO
+SUBS.
+
+\ENDDOC
 \DOC{SUBST\_MATCH}
 
 \TYPE {\small\verb%SUBST_MATCH : (thm -> thm -> thm)%}\egroup
@@ -25738,89 +25831,38 @@
 {\small\verb%vi%} becoming bound after substitution.
 
 \FAILURE
-{\small\verb%SUBST_TAC [th1;...;thn] (A,t)%} fails if the conclusion of any theorem in the
-list is not an equation.  No change is made to the goal if no occurrence of the
-left-hand side of the conclusion of {\small\verb%thi%} appears in {\small\verb%t%}.
-
-\EXAMPLE
-When trying to solve the goal
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ?- (n + 0) + (0 + m) = m + n
-\end{verbatim}
-}
-\noindent by substituting with the theorems
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #let thm1 = SPECL ["m:num"; "n:num"] ADD_SYM
-   #and thm2 = CONJUNCT1 ADD_CLAUSES;;
-   thm1 = |- m + n = n + m
-   thm2 = |- 0 + m = m
-\end{verbatim}
-}
-\noindent applying {\small\verb%SUBST_TAC [thm1; thm2]%} results in the goal
-{\par\samepage\setseps\small
-\begin{verbatim}
-   ?- (n + 0) + m = n + m
-\end{verbatim}
-}
-\USES
-{\small\verb%SUBST_TAC%} is used when rewriting (for example, with {\small\verb%REWRITE_TAC%}) is
-extensive or would diverge.  Substituting is also much faster than rewriting.
-
-\SEEALSO
-ONCE_REWRITE_TAC, PURE_REWRITE_TAC, REWRITE_TAC, SUBST1_TAC, SUBST_ALL_TAC.
-
-\ENDDOC
-\DOC{SUBS\_OCCS}
-
-\TYPE {\small\verb%SUBS_OCCS : ((int list # thm) list -> thm -> thm)%}\egroup
-
-\SYNOPSIS
-Makes substitutions in a theorem at specific occurrences of a term, using a
-list of equational theorems.
-
-\DESCRIBE
-Given a list {\small\verb%(l1,A1|-t1=v1),...,(ln,An|-tn=vn)%} and a theorem
-{\small\verb%(A|-t)%}, {\small\verb%SUBS_OCCS%} simultaneously replaces each {\small\verb%ti%} in {\small\verb%t%} with {\small\verb%vi%},
-at the occurrences specified by the integers
-in the list {\small\verb%li = [o1;...;ok]%} for each theorem {\small\verb%Ai|-ti=vi%}.
+{\small\verb%SUBST_TAC [th1;...;thn] (A,t)%} fails if the conclusion of any theorem in the
+list is not an equation.  No change is made to the goal if no occurrence of the
+left-hand side of the conclusion of {\small\verb%thi%} appears in {\small\verb%t%}.
+
+\EXAMPLE
+When trying to solve the goal
 {\par\samepage\setseps\small
 \begin{verbatim}
-     (l1,A1|-t1=v1) ... (ln,An|-tn=vn)  A|-t
-   -------------------------------------------  SUBS_OCCS[(l1,A1|-t1=v1);...;
-    A1 u ... An u A |- t[v1,...,vn/t1,...,tn]            (ln,An|-tn=vn)] (A|-t)
+   ?- (n + 0) + (0 + m) = m + n
 \end{verbatim}
 }
-\FAILURE
-{\small\verb%SUBS_OCCS [(l1,th1);...;(ln,thn)] (A|-t)%} fails if
-the conclusion of any theorem in the list is not an equation.
-No change is made to the theorem if the supplied occurrences {\small\verb%li%} of the
-left-hand side of the conclusion of {\small\verb%thi%} do not appear in {\small\verb%t%}.
-
-\EXAMPLE
-The commutative law for addition
+\noindent by substituting with the theorems
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #let thm = SPECL ["m:num"; "n:num"] ADD_SYM;;
-   thm = |- m + n = n + m
+   #let thm1 = SPECL ["m:num"; "n:num"] ADD_SYM
+   #and thm2 = CONJUNCT1 ADD_CLAUSES;;
+   thm1 = |- m + n = n + m
+   thm2 = |- 0 + m = m
 \end{verbatim}
 }
-\noindent can be used for substituting only the second occurrence of
-the subterm {\small\verb%m + n%}
+\noindent applying {\small\verb%SUBST_TAC [thm1; thm2]%} results in the goal
 {\par\samepage\setseps\small
 \begin{verbatim}
-   #SUBS_OCCS [([2],thm)] (ASSUME "(n + m) + (m + n) = (m + n) + (m + n)");;
-   . |- (n + m) + (m + n) = (n + m) + (m + n)
+   ?- (n + 0) + m = n + m
 \end{verbatim}
 }
 \USES
-{\small\verb%SUBS_OCCS%} is used when rewriting at specific occurrences of a term, and rules
-such as {\small\verb%REWRITE_RULE%}, {\small\verb%PURE_REWRITE_RULE%}, {\small\verb%ONCE_REWRITE_RULE%}, and {\small\verb%SUBS%}
-are too extensive or would diverge.
+{\small\verb%SUBST_TAC%} is used when rewriting (for example, with {\small\verb%REWRITE_TAC%}) is
+extensive or would diverge.  Substituting is also much faster than rewriting.
 
 \SEEALSO
-ONCE_REWRITE_RULE, PURE_REWRITE_RULE, REWRITE_RULE, SUBS, SUBST, SUBST_MATCH.
+ONCE_REWRITE_TAC, PURE_REWRITE_TAC, REWRITE_TAC, SUBST1_TAC, SUBST_ALL_TAC.
 
 \ENDDOC
 \DOC{subtract}
@@ -25851,50 +25893,6 @@
 setify, set_equal, union, intersect.
 
 \ENDDOC
-\DOC{SUB\_CONV}
-
-\TYPE {\small\verb%SUB_CONV : (conv -> conv)%}\egroup
-
-\SYNOPSIS
-Applies a conversion to the top-level subterms of a term.
-
-\DESCRIBE
-For any conversion {\small\verb%c%}, the function returned by {\small\verb%SUB_CONV c%} is a conversion
-that applies {\small\verb%c%} to all the top-level subterms of a term.  If the conversion
-{\small\verb%c%} maps {\small\verb%t%} to {\small\verb%|- t = t'%}, then {\small\verb%SUB_CONV c%} maps an abstraction {\small\verb%"\x.t"%} to
-the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (\x.t) = (\x.t')
-\end{verbatim}
-}
-\noindent That is, {\small\verb%SUB_CONV c "\x.t"%} applies {\small\verb%c%} to the body of the
-abstraction {\small\verb%"\x.t"%}.  If {\small\verb%c%} is a conversion that maps {\small\verb%"t1"%} to the theorem
-{\small\verb%|- t1 = t1'%} and {\small\verb%"t2"%} to the theorem {\small\verb%|- t2 = t2'%}, then the conversion
-{\small\verb%SUB_CONV c%} maps an application {\small\verb%"t1 t2"%} to the theorem:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   |- (t1 t2) = (t1' t2')
-\end{verbatim}
-}
-\noindent That is, {\small\verb%SUB_CONV c "t1 t2"%} applies {\small\verb%c%} to the both the operator
-{\small\verb%t1%} and the operand {\small\verb%t2%} of the application {\small\verb%"t1 t2"%}.  Finally, for any
-conversion {\small\verb%c%}, the function returned by {\small\verb%SUB_CONV c%} acts as the identity
-conversion on variables and constants.  That is, if {\small\verb%"t"%} is a variable or
-constant, then {\small\verb%SUB_CONV c "t"%} returns {\small\verb%|- t = t%}.
-
-\FAILURE
-{\small\verb%SUB_CONV c tm%} fails if {\small\verb%tm%} is an abstraction {\small\verb%"\x.t"%} and the conversion {\small\verb%c%}
-fails when applied to {\small\verb%t%}, or if {\small\verb%tm%} is an application {\small\verb%"t1 t2"%} and the
-conversion {\small\verb%c%} fails when applied to either {\small\verb%t1%} or {\small\verb%t2%}.  The function
-returned by {\small\verb%SUB_CONV c%} may also fail if the ML function {\small\verb%c:term->thm%} is not,
-in fact, a conversion (i.e. a function that maps a term {\small\verb%t%} to a theorem
-{\small\verb%|- t = t'%}).
-
-\SEEALSO
-ABS_CONV, RAND_CONV, RATOR_CONV.
-
-\ENDDOC
 \DOC{suspend\_recording}
 
 \TYPE {\small\verb%suspend_recording : void -> void%}\egroup
@@ -25958,50 +25956,50 @@
 {\small\verb%?x y. P%}.
 
 \ENDDOC
-\DOC{SYM}
+\DOC{SYM\_CONV}
 
-\TYPE {\small\verb%SYM : (thm -> thm)%}\egroup
+\TYPE {\small\verb%SYM_CONV : conv%}\egroup
 
 \SYNOPSIS
-Swaps left-hand and right-hand sides of an equation.
+Interchanges the left and right-hand sides of an equation.
 
 \DESCRIBE
-When applied to a theorem {\small\verb%A |- t1 = t2%}, the inference rule {\small\verb%SYM%} returns
-{\small\verb%A |- t2 = t1%}.
+When applied to an equational term {\small\verb%t1 = t2%}, the conversion
+{\small\verb%SYM_CONV%} returns the theorem:
 {\par\samepage\setseps\small
 \begin{verbatim}
-    A |- t1 = t2
-   --------------  SYM
-    A |- t2 = t1
+   |- (t1 = t2) = (t2 = t1)
 \end{verbatim}
 }
 \FAILURE
-Fails unless the theorem is equational.
+Fails if applied to a term that is not an equation.
 
 \SEEALSO
-GSYM, NOT_EQ_SYM, REFL.
+SYM.
 
 \ENDDOC
-\DOC{SYM\_CONV}
+\DOC{SYM}
 
-\TYPE {\small\verb%SYM_CONV : conv%}\egroup
+\TYPE {\small\verb%SYM : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Interchanges the left and right-hand sides of an equation.
+Swaps left-hand and right-hand sides of an equation.
 
 \DESCRIBE
-When applied to an equational term {\small\verb%t1 = t2%}, the conversion
-{\small\verb%SYM_CONV%} returns the theorem:
+When applied to a theorem {\small\verb%A |- t1 = t2%}, the inference rule {\small\verb%SYM%} returns
+{\small\verb%A |- t2 = t1%}.
 {\par\samepage\setseps\small
 \begin{verbatim}
-   |- (t1 = t2) = (t2 = t1)
+    A |- t1 = t2
+   --------------  SYM
+    A |- t2 = t1
 \end{verbatim}
 }
 \FAILURE
-Fails if applied to a term that is not an equation.
+Fails unless the theorem is equational.
 
 \SEEALSO
-SYM.
+GSYM, NOT_EQ_SYM, REFL.
 
 \ENDDOC
 \DOC{syserror}
@@ -26100,6 +26098,31 @@
 int_of_term, int_of_string, string_of_int.
 
 \ENDDOC
+\DOC{THENC}
+
+\TYPE {\small\verb%$THENC : (conv -> conv -> conv)%}\egroup
+
+\SYNOPSIS
+Applies two conversions in sequence.
+
+\DESCRIBE
+If the conversion {\small\verb%c1%} returns {\small\verb%|- t = t'%} when applied to a term {\small\verb%"t"%}, and
+{\small\verb%c2%} returns {\small\verb%|- t' = t''%} when applied to {\small\verb%"t'"%}, then the composite
+conversion {\small\verb%(c1 THENC c2) "t"%} returns {\small\verb%|- t = t''%}.  That is, {\small\verb%(c1 THENC c2)
+"t"%} has the effect of transforming the term {\small\verb%"t"%} first with the conversion
+{\small\verb%c1%} and then with the conversion {\small\verb%c2%}.
+
+\FAILURE
+{\small\verb%(c1 THENC c2) "t"%} fails if either the conversion {\small\verb%c1%} fails when applied to
+{\small\verb%"t"%}, or if {\small\verb%c1 "t"%} succeeds and returns {\small\verb%|- t = t'%} but {\small\verb%c2%} fails when
+applied to {\small\verb%"t'"%}.  {\small\verb%(c1 THENC c2) "t"%} may also fail if either of {\small\verb%c1%} or {\small\verb%c2%}
+is not, in fact, a conversion (i.e. a function that maps a term {\small\verb%t%} to a
+theorem {\small\verb%|- t = t'%}).
+
+\SEEALSO
+EVERY_CONV.
+
+\ENDDOC
 \DOC{THEN}
 
 \TYPE {\small\verb%$THEN : (tactic -> tactic -> tactic)%}\egroup
@@ -26136,31 +26159,6 @@
 EVERY, ORELSE, THENL.
 
 \ENDDOC
-\DOC{THENC}
-
-\TYPE {\small\verb%$THENC : (conv -> conv -> conv)%}\egroup
-
-\SYNOPSIS
-Applies two conversions in sequence.
-
-\DESCRIBE
-If the conversion {\small\verb%c1%} returns {\small\verb%|- t = t'%} when applied to a term {\small\verb%"t"%}, and
-{\small\verb%c2%} returns {\small\verb%|- t' = t''%} when applied to {\small\verb%"t'"%}, then the composite
-conversion {\small\verb%(c1 THENC c2) "t"%} returns {\small\verb%|- t = t''%}.  That is, {\small\verb%(c1 THENC c2)
-"t"%} has the effect of transforming the term {\small\verb%"t"%} first with the conversion
-{\small\verb%c1%} and then with the conversion {\small\verb%c2%}.
-
-\FAILURE
-{\small\verb%(c1 THENC c2) "t"%} fails if either the conversion {\small\verb%c1%} fails when applied to
-{\small\verb%"t"%}, or if {\small\verb%c1 "t"%} succeeds and returns {\small\verb%|- t = t'%} but {\small\verb%c2%} fails when
-applied to {\small\verb%"t'"%}.  {\small\verb%(c1 THENC c2) "t"%} may also fail if either of {\small\verb%c1%} or {\small\verb%c2%}
-is not, in fact, a conversion (i.e. a function that maps a term {\small\verb%t%} to a
-theorem {\small\verb%|- t = t'%}).
-
-\SEEALSO
-EVERY_CONV.
-
-\ENDDOC
 \DOC{THENL}
 
 \TYPE {\small\verb%$THENL : (tactic -> tactic list -> tactic)%}\egroup
@@ -26253,41 +26251,6 @@
 theorems.
 
 \ENDDOC
-\DOC{theorems}
-
-\TYPE {\small\verb%theorems : (string -> (string # thm) list)%}\egroup
-
-\SYNOPSIS
-Returns the derived theorems of a given theory segment of the current theory.
-
-\DESCRIBE
-A call of {\small\verb%theorems `thy`%} returns the derived theorems of the theory segment
-{\small\verb%thy%} together with their names. The theory segment {\small\verb%thy%} must be part of
-the current theory. The names are those given to the theorems by the user when
-they were originally added to the theory segment (by, for example, a call to
-{\small\verb%save_thm%}). The name of the current theory segment can be abbreviated by {\small\verb%`-`%}.
-
-\FAILURE
-The call {\small\verb%theorems `thy`%} will fail if the theory segment {\small\verb%thy%} is not part
-of the current theory.
-
-\EXAMPLE
-{\par\samepage\setseps\small
-\begin{verbatim}
-#theorems `bool`;;
-[(`PAIR_EQ`, |- !x y a b. (x,y = a,b) = (x = a) /\ (y = b));
- (`SND`, |- !x y. SND(x,y) = y);
- (`FST`, |- !x y. FST(x,y) = x);
- (`PAIR`, |- !x. FST x,SND x = x);
- (`PAIR_EXISTS`, |- ?p. IS_PAIR p)]
-: (string # thm) list
-\end{verbatim}
-}
-\SEEALSO
-axioms, definitions, load_theorem, load_theorems, print_theory, save_thm,
-theorem.
-
-\ENDDOC
 \DOC{theorem\_lfn}
 
 \TYPE {\small\verb%theorem_lfn : (string list -> thm)%}\egroup
@@ -26362,6 +26325,41 @@
 load_theorems, undo_autoload.
 
 \ENDDOC
+\DOC{theorems}
+
+\TYPE {\small\verb%theorems : (string -> (string # thm) list)%}\egroup
+
+\SYNOPSIS
+Returns the derived theorems of a given theory segment of the current theory.
+
+\DESCRIBE
+A call of {\small\verb%theorems `thy`%} returns the derived theorems of the theory segment
+{\small\verb%thy%} together with their names. The theory segment {\small\verb%thy%} must be part of
+the current theory. The names are those given to the theorems by the user when
+they were originally added to the theory segment (by, for example, a call to
+{\small\verb%save_thm%}). The name of the current theory segment can be abbreviated by {\small\verb%`-`%}.
+
+\FAILURE
+The call {\small\verb%theorems `thy`%} will fail if the theory segment {\small\verb%thy%} is not part
+of the current theory.
+
+\EXAMPLE
+{\par\samepage\setseps\small
+\begin{verbatim}
+#theorems `bool`;;
+[(`PAIR_EQ`, |- !x y a b. (x,y = a,b) = (x = a) /\ (y = b));
+ (`SND`, |- !x y. SND(x,y) = y);
+ (`FST`, |- !x y. FST(x,y) = x);
+ (`PAIR`, |- !x. FST x,SND x = x);
+ (`PAIR_EXISTS`, |- ?p. IS_PAIR p)]
+: (string # thm) list
+\end{verbatim}
+}
+\SEEALSO
+axioms, definitions, load_theorem, load_theorems, print_theory, save_thm,
+theorem.
+
+\ENDDOC
 \DOC{thm\_count}
 
 \TYPE {\small\verb%thm_count : (void -> int)%}\egroup
@@ -26653,15 +26651,36 @@
    t1 = . |- a = b
    t2 = . |- b = c
 
-   #TRANS t1 t2;;
-   .. |- a = c
+   #TRANS t1 t2;;
+   .. |- a = c
+
+   #t1 TRANS t2;;
+   .. |- a = c
+\end{verbatim}
+}
+\SEEALSO
+EQ_MP, IMP_TRANS, REFL, SYM.
+
+\ENDDOC
+\DOC{TRY\_CONV}
+
+\TYPE {\small\verb%TRY_CONV : (conv -> conv)%}\egroup
+
+\SYNOPSIS
+Attempts to apply a conversion; applies identity conversion in case of failure.
+
+\DESCRIBE
+{\small\verb%TRY_CONV c "t"%} attempts to apply the conversion {\small\verb%c%} to the term {\small\verb%"t"%}; if
+this fails, then the identity conversion applied instead.  That is, if {\small\verb%c%} is a
+conversion that maps a term {\small\verb%"t"%} to the theorem {\small\verb%|- t = t'%}, then the
+conversion {\small\verb%TRY_CONV c%} also maps {\small\verb%"t"%} to {\small\verb%|- t = t'%}. But if {\small\verb%c%} fails when
+applied to {\small\verb%"t"%}, then {\small\verb%TRY_CONV c "t"%} returns {\small\verb%|- t = t%}.
+
+\FAILURE
+Never fails.
 
-   #t1 TRANS t2;;
-   .. |- a = c
-\end{verbatim}
-}
 \SEEALSO
-EQ_MP, IMP_TRANS, REFL, SYM.
+ALL_CONV.
 
 \ENDDOC
 \DOC{TRY}
@@ -26704,27 +26723,6 @@
 find, mem, exists, forall, assoc, rev_assoc.
 
 \ENDDOC
-\DOC{TRY\_CONV}
-
-\TYPE {\small\verb%TRY_CONV : (conv -> conv)%}\egroup
-
-\SYNOPSIS
-Attempts to apply a conversion; applies identity conversion in case of failure.
-
-\DESCRIBE
-{\small\verb%TRY_CONV c "t"%} attempts to apply the conversion {\small\verb%c%} to the term {\small\verb%"t"%}; if
-this fails, then the identity conversion applied instead.  That is, if {\small\verb%c%} is a
-conversion that maps a term {\small\verb%"t"%} to the theorem {\small\verb%|- t = t'%}, then the
-conversion {\small\verb%TRY_CONV c%} also maps {\small\verb%"t"%} to {\small\verb%|- t = t'%}. But if {\small\verb%c%} fails when
-applied to {\small\verb%"t"%}, then {\small\verb%TRY_CONV c "t"%} returns {\small\verb%|- t = t%}.
-
-\FAILURE
-Never fails.
-
-\SEEALSO
-ALL_CONV.
-
-\ENDDOC
 \DOC{tty\_read}
 
 \TYPE {\small\verb%tty_read : (void -> string)%}\egroup
@@ -26780,53 +26778,6 @@
 append_openw, close, openi, openw, read, tty_read, write.
 
 \ENDDOC
-\DOC{types}
-
-\TYPE {\small\verb%types : (string -> (int # string) list)%}\egroup
-
-\SYNOPSIS
-Lists the types in the named theory.
-
-\DESCRIBE
-The function {\small\verb%types%} should be applied to a string which is the name of an
-ancestor theory (including the current theory; the special string {\small\verb%`-`%} is
-always interpreted as the current theory). It returns a list of all the
-type constructors declared in the named theory, in the form of arity-name
-pairs.
-
-\FAILURE
-Fails unless the named theory is an ancestor.
-
-\EXAMPLE
-The theory {\small\verb%HOL%} has no types declared:
-{\par\samepage\setseps\small
-\begin{verbatim}
-  #types `HOL`;;
-  [] : (int # string) list
-\end{verbatim}
-}
-\noindent but its ancestors have the following types declared:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   #itlist union (map types (ancestors `HOL`)) [];;
-   [(2, `fun`);
-    (2, `prod`);
-    (0, `bool`);
-    (0, `ind`);
-    (0, `num`);
-    (1, `list`);
-    (0, `tree`);
-    (1, `ltree`);
-    (2, `sum`);
-    (0, `one`)]
-   : (int # string) list
-\end{verbatim}
-}
-\SEEALSO
-ancestors, axioms, constants, definitions, infixes, new_type, new_type_abbrev,
-new_type_definition, parents.
-
-\ENDDOC
 \DOC{type\_abbrevs}
 
 \TYPE {\small\verb%type_abbrevs : (string -> (string # type) list)%}\egroup
@@ -26936,6 +26887,53 @@
 \end{verbatim}
 }
 \ENDDOC
+\DOC{types}
+
+\TYPE {\small\verb%types : (string -> (int # string) list)%}\egroup
+
+\SYNOPSIS
+Lists the types in the named theory.
+
+\DESCRIBE
+The function {\small\verb%types%} should be applied to a string which is the name of an
+ancestor theory (including the current theory; the special string {\small\verb%`-`%} is
+always interpreted as the current theory). It returns a list of all the
+type constructors declared in the named theory, in the form of arity-name
+pairs.
+
+\FAILURE
+Fails unless the named theory is an ancestor.
+
+\EXAMPLE
+The theory {\small\verb%HOL%} has no types declared:
+{\par\samepage\setseps\small
+\begin{verbatim}
+  #types `HOL`;;
+  [] : (int # string) list
+\end{verbatim}
+}
+\noindent but its ancestors have the following types declared:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   #itlist union (map types (ancestors `HOL`)) [];;
+   [(2, `fun`);
+    (2, `prod`);
+    (0, `bool`);
+    (0, `ind`);
+    (0, `num`);
+    (1, `list`);
+    (0, `tree`);
+    (1, `ltree`);
+    (2, `sum`);
+    (0, `one`)]
+   : (int # string) list
+\end{verbatim}
+}
+\SEEALSO
+ancestors, axioms, constants, definitions, infixes, new_type, new_type_abbrev,
+new_type_definition, parents.
+
+\ENDDOC
 \DOC{type\_tyvars}
 
 \TYPE {\small\verb%type_tyvars : (type -> type list)%}\egroup
@@ -27051,68 +27049,68 @@
 curry.
 
 \ENDDOC
-\DOC{UNDISCH}
+\DOC{UNDISCH\_ALL}
 
-\TYPE {\small\verb%UNDISCH : (thm -> thm)%}\egroup
+\TYPE {\small\verb%UNDISCH_ALL : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Undischarges the antecedent of an implicative theorem.
+Iteratively undischarges antecedents in a chain of implications.
 
 \DESCRIBE
 {\par\samepage\setseps\small
 \begin{verbatim}
-    A |- t1 ==> t2
-   ----------------  UNDISCH
-     A, t1 |- t2
+    A |- t1 ==> ... ==> tn ==> t
+   ------------------------------  UNDISCH_ALL
+        A, t1, ..., tn |- t
 \end{verbatim}
 }
-\noindent Note that {\small\verb%UNDISCH%} treats {\small\verb%"~u"%} as {\small\verb%"u ==> F"%}.
+\noindent Note that {\small\verb%UNDISCH_ALL%} treats {\small\verb%"~u"%} as {\small\verb%"u ==> F"%}.
 
 \FAILURE
-{\small\verb%UNDISCH%} will fail on theorems which are not implications or negations.
+Unlike {\small\verb%UNDISCH%}, {\small\verb%UNDISCH_ALL%} will,
+when called on something other than an implication or negation,
+return its argument unchanged rather than failing.
 
 \COMMENTS
-If the antecedent already appears in the hypotheses, it will not be duplicated.
-However, unlike {\small\verb%DISCH%},
-if the antecedent is alpha-equivalent to one of the hypotheses,
-it will still be added to the hypotheses.
+Identical terms which are repeated in {\small\verb%A, "t1", ..., "tn"%} will
+not be duplicated in the hypotheses of the resulting theorem.
+However, if two or more alpha-equivalent terms appear in {\small\verb%A, "t1", ..., "tn"%},
+then each distinct term will appear in the result.
 
 \SEEALSO
-DISCH, DISCH_ALL, DISCH_TAC, DISCH_THEN, FILTER_DISCH_TAC, FILTER_DISCH_THEN,
-NEG_DISCH, STRIP_TAC, UNDISCH_ALL, UNDISCH_TAC.
+DISCH, DISCH_ALL, DISCH_TAC, DISCH_THEN, NEG_DISCH, FILTER_DISCH_TAC,
+FILTER_DISCH_THEN, STRIP_TAC, UNDISCH, UNDISCH_TAC.
 
 \ENDDOC
-\DOC{UNDISCH\_ALL}
+\DOC{UNDISCH}
 
-\TYPE {\small\verb%UNDISCH_ALL : (thm -> thm)%}\egroup
+\TYPE {\small\verb%UNDISCH : (thm -> thm)%}\egroup
 
 \SYNOPSIS
-Iteratively undischarges antecedents in a chain of implications.
+Undischarges the antecedent of an implicative theorem.
 
 \DESCRIBE
 {\par\samepage\setseps\small
 \begin{verbatim}
-    A |- t1 ==> ... ==> tn ==> t
-   ------------------------------  UNDISCH_ALL
-        A, t1, ..., tn |- t
+    A |- t1 ==> t2
+   ----------------  UNDISCH
+     A, t1 |- t2
 \end{verbatim}
 }
-\noindent Note that {\small\verb%UNDISCH_ALL%} treats {\small\verb%"~u"%} as {\small\verb%"u ==> F"%}.
+\noindent Note that {\small\verb%UNDISCH%} treats {\small\verb%"~u"%} as {\small\verb%"u ==> F"%}.
 
 \FAILURE
-Unlike {\small\verb%UNDISCH%}, {\small\verb%UNDISCH_ALL%} will,
-when called on something other than an implication or negation,
-return its argument unchanged rather than failing.
+{\small\verb%UNDISCH%} will fail on theorems which are not implications or negations.
 
 \COMMENTS
-Identical terms which are repeated in {\small\verb%A, "t1", ..., "tn"%} will
-not be duplicated in the hypotheses of the resulting theorem.
-However, if two or more alpha-equivalent terms appear in {\small\verb%A, "t1", ..., "tn"%},
-then each distinct term will appear in the result.
+If the antecedent already appears in the hypotheses, it will not be duplicated.
+However, unlike {\small\verb%DISCH%},
+if the antecedent is alpha-equivalent to one of the hypotheses,
+it will still be added to the hypotheses.
 
 \SEEALSO
-DISCH, DISCH_ALL, DISCH_TAC, DISCH_THEN, NEG_DISCH, FILTER_DISCH_TAC,
-FILTER_DISCH_THEN, STRIP_TAC, UNDISCH, UNDISCH_TAC.
+DISCH, DISCH_ALL, DISCH_TAC, DISCH_THEN, FILTER_DISCH_TAC, FILTER_DISCH_THEN,
+NEG_DISCH, STRIP_TAC, UNDISCH_ALL, UNDISCH_TAC.
 
 \ENDDOC
 \DOC{UNDISCH\_TAC}
@@ -27424,18 +27422,21 @@
 \#, B, C, CB, Co, I, K, KI, o, oo, S.
 
 \ENDDOC
-\DOC{words}
+\DOC{words2}
 
-\TYPE {\small\verb%words : (string -> string list)%}\egroup
+\TYPE {\small\verb%words2 : (string -> string -> string list)%}\egroup
 
 \SYNOPSIS
-Splits a string into a list of words.
+Splits a string into a list of substrings, breaking at occurrences of a
+specified character.
 
 \DESCRIBE
-{\small\verb%words s%} splits the string {\small\verb%s%} into a list of substrings. Splitting occurs
-at each sequence of blanks and carriage returns (white space). This white
-space does not appear in the list of substrings. Leading and trailing white
-space in the input string is also thrown away.
+{\small\verb%words2 char s%} splits the string {\small\verb%s%} into a list of substrings. Splitting
+occurs at each occurrence of a sequence of the character {\small\verb%char%}. The {\small\verb%char%}
+characters do not appear in the list of substrings. Leading and trailing
+occurrences of {\small\verb%char%} are also thrown away. If {\small\verb%char%} is not a
+single-character string (its length is not 1), then {\small\verb%s%} will not be split and
+so the result will be the list {\small\verb%[s]%}.
 
 \FAILURE
 Never fails.
@@ -27443,37 +27444,29 @@
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#words `  the cat  sat on   the mat `;;
+#words2 `/` `/the/cat//sat/on//the/mat/`;;
 [`the`; `cat`; `sat`; `on`; `the`; `mat`] : string list
-\end{verbatim}
-}
-\USES
-Useful when wanting to map a function over a list of constant strings.
-Instead of using {\small\verb%[`string1`;...;`stringn`]%} one can use:
-{\par\samepage\setseps\small
-\begin{verbatim}
-   (words `string1 ... stringn`)
+
+#words2 `//` `/the/cat//sat/on//the/mat/`;;
+[`/the/cat//sat/on//the/mat/`] : string list
 \end{verbatim}
 }
 \SEEALSO
-words2, word_separators, maptok, explode.
+words, word_separators, explode.
 
 \ENDDOC
-\DOC{words2}
+\DOC{words}
 
-\TYPE {\small\verb%words2 : (string -> string -> string list)%}\egroup
+\TYPE {\small\verb%words : (string -> string list)%}\egroup
 
 \SYNOPSIS
-Splits a string into a list of substrings, breaking at occurrences of a
-specified character.
+Splits a string into a list of words.
 
 \DESCRIBE
-{\small\verb%words2 char s%} splits the string {\small\verb%s%} into a list of substrings. Splitting
-occurs at each occurrence of a sequence of the character {\small\verb%char%}. The {\small\verb%char%}
-characters do not appear in the list of substrings. Leading and trailing
-occurrences of {\small\verb%char%} are also thrown away. If {\small\verb%char%} is not a
-single-character string (its length is not 1), then {\small\verb%s%} will not be split and
-so the result will be the list {\small\verb%[s]%}.
+{\small\verb%words s%} splits the string {\small\verb%s%} into a list of substrings. Splitting occurs
+at each sequence of blanks and carriage returns (white space). This white
+space does not appear in the list of substrings. Leading and trailing white
+space in the input string is also thrown away.
 
 \FAILURE
 Never fails.
@@ -27481,15 +27474,20 @@
 \EXAMPLE
 {\par\samepage\setseps\small
 \begin{verbatim}
-#words2 `/` `/the/cat//sat/on//the/mat/`;;
+#words `  the cat  sat on   the mat `;;
 [`the`; `cat`; `sat`; `on`; `the`; `mat`] : string list
-
-#words2 `//` `/the/cat//sat/on//the/mat/`;;
-[`/the/cat//sat/on//the/mat/`] : string list
+\end{verbatim}
+}
+\USES
+Useful when wanting to map a function over a list of constant strings.
+Instead of using {\small\verb%[`string1`;...;`stringn`]%} one can use:
+{\par\samepage\setseps\small
+\begin{verbatim}
+   (words `string1 ... stringn`)
 \end{verbatim}
 }
 \SEEALSO
-words, word_separators, explode.
+words2, word_separators, maptok, explode.
 
 \ENDDOC
 \DOC{word\_separators}
--- hol88-2.02.19940316.orig/Manual/Reference/reference.tex
+++ hol88-2.02.19940316/Manual/Reference/reference.tex
@@ -32,7 +32,7 @@
 
    \include{title}			  % reference title page
    \include{preface}			  % preface to reference manual
-   \include{../LaTeX/ack}		  % global acknowledgements
+   \include{ack}		          % global acknowledgements
    \include{contents}			  % table of contents
 
    % ---------------------------------------------------------------------
--- hol88-2.02.19940316.orig/Manual/Reference/theorems.tex
+++ hol88-2.02.19940316/Manual/Reference/theorems.tex
@@ -1,7 +1,4 @@
-\chapter{Pre-proved Theorems}
-\input{theorems-intro}
-\section{Definitions of Basic Logical Constants}
-\THEOREM AND\_DEF bool
+\chapter{Pre-proved Theorems}\input{theorems-intro}\section{Definitions of Basic Logical Constants}\THEOREM AND\_DEF bool
 |- $/\ = (\t1 t2. !t. (t1 ==> t2 ==> t) ==> t)
 \ENDTHEOREM
 \THEOREM EXISTS\_DEF bool
@@ -10,12 +7,12 @@
 \THEOREM EXISTS\_UNIQUE\_DEF bool
 |- $?! = (\P. $? P /\ (!x y. P x /\ P y ==> (x = y)))
 \ENDTHEOREM
-\THEOREM FORALL\_DEF bool
-|- $! = (\P. P = (\x. T))
-\ENDTHEOREM
 \THEOREM F\_DEF bool
 |- F = (!t. t)
 \ENDTHEOREM
+\THEOREM FORALL\_DEF bool
+|- $! = (\P. P = (\x. T))
+\ENDTHEOREM
 \THEOREM NOT\_DEF bool
 |- $~ = (\t. t ==> F)
 \ENDTHEOREM
@@ -25,8 +22,7 @@
 \THEOREM T\_DEF bool
 |- T = ((\x. x) = (\x. x))
 \ENDTHEOREM
-\section{Constants for syntactic abbreviations}
-\THEOREM ARB bool
+\section{Constants for syntactic abbreviations}\THEOREM ARB bool
 |- ARB = (@x. T)
 \ENDTHEOREM
 \THEOREM COND\_DEF bool
@@ -49,8 +45,7 @@
 \THEOREM RES\_SELECT bool
 |- !P B. RES_SELECT P B = (@x. P x /\ B x)
 \ENDTHEOREM
-\section{Axioms}
-\THEOREM ARB\_THM bool
+\section{Axioms}\THEOREM ARB\_THM bool
 |- $= = $=
 \ENDTHEOREM
 \THEOREM BOOL\_CASES\_AX bool
@@ -68,8 +63,7 @@
 \THEOREM SELECT\_AX bool
 |- !P x. P x ==> P($@ P)
 \ENDTHEOREM
-\section{Logical tautologies}
-\THEOREM AND1\_THM {\none}
+\section{Logical tautologies}\THEOREM AND1\_THM {\none}
 |- !t1 t2. t1 /\ t2 ==> t1 
 \ENDTHEOREM
 \THEOREM AND2\_THM {\none}
@@ -171,13 +165,13 @@
 \THEOREM FALSITY {\none}
 |- !t. F ==> t
 \ENDTHEOREM
+\THEOREM F\_IMP {\none}
+|- !t. ~t ==>(t ==> F)
+\ENDTHEOREM
 \THEOREM FORALL\_SIMP {\none}
 |- !t. (!x. t) = t
 \ENDTHEOREM
 
-\THEOREM F\_IMP {\none}
-|- !t. ~t ==>(t ==> F)
-\ENDTHEOREM
 \THEOREM IMP\_CLAUSES {\none}
 |- !t. (T ==> t) = t /\
        (t ==> T) = T /\
@@ -258,8 +252,7 @@
 \THEOREM TRUTH {\none}
 |- T
 \ENDTHEOREM
-\section{Theorems about functions}
-\THEOREM ABS\_SIMP {\none}
+\section{Theorems about functions}\THEOREM ABS\_SIMP {\none}
 |- !t1 t2. (\x. t1)t2 = t1
 \ENDTHEOREM
 
@@ -309,24 +302,22 @@
 \THEOREM RIGHT\_ID\_DEF fun
 |- !f e. RIGHT_ID f e = (!x. f x e = x)
 \ENDTHEOREM
-\section{Theorems about the type {\tt one}}
-\THEOREM one one
-|- !v. v = one
+\section{Theorems about the type {\tt one}}\THEOREM one\_axiom one
+|- !f g. f = g
 \ENDTHEOREM
 \THEOREM one\_Axiom one
 |- !e. ?! fn. fn one = e
 \ENDTHEOREM
-\THEOREM one\_axiom one
-|- !f g. f = g
-\ENDTHEOREM
 \THEOREM one\_DEF one
 |- one = (@x. T)
 \ENDTHEOREM
+\THEOREM one one
+|- !v. v = one
+\ENDTHEOREM
 \THEOREM one\_TY\_DEF one
 |- ?rep. TYPE_DEFINITION(\b. b)rep
 \ENDTHEOREM
-\section{Theorems about combinators}
-\THEOREM I\_DEF combin
+\section{Theorems about combinators}\THEOREM I\_DEF combin
 |- I = S K K
 \ENDTHEOREM
 \THEOREM I\_o\_ID combin
@@ -356,19 +347,18 @@
 \THEOREM S\_THM combin
 |- !f g x. S f g x = f x(g x)
 \ENDTHEOREM
-\section{Theorems about pairs}
-\THEOREM COMMA\_DEF bool
+\section{Theorems about pairs}\THEOREM COMMA\_DEF bool
 |- !x y. x,y = (@p. REP_prod p = MK_PAIR x y)
 \ENDTHEOREM
 \THEOREM CURRY\_DEF bool
 |- !f x y. CURRY f x y = f(x,y)
 \ENDTHEOREM
-\THEOREM FST bool
-|- !x y. FST(x,y) = x
-\ENDTHEOREM
 \THEOREM FST\_DEF bool
 |- !p. FST p = (@x. ?y. MK_PAIR x y = REP_prod p)
 \ENDTHEOREM
+\THEOREM FST bool
+|- !x y. FST(x,y) = x
+\ENDTHEOREM
 \THEOREM IS\_PAIR\_DEF bool
 |- !p. IS_PAIR p = (?x y. p = MK_PAIR x y)
 \ENDTHEOREM
@@ -390,28 +380,27 @@
      (!p' p''. (rep p' = rep p'') ==> (p' = p'')) /\
      (!p. IS_PAIR p = (?p'. p = rep p')))
 \ENDTHEOREM
-\THEOREM SND bool
-|- !x y. SND(x,y) = y
-\ENDTHEOREM
 \THEOREM SND\_DEF bool
 |- !p. SND p = (@y. ?x. MK_PAIR x y = REP_prod p)
 \ENDTHEOREM
+\THEOREM SND bool
+|- !x y. SND(x,y) = y
+\ENDTHEOREM
 \THEOREM UNCURRY\_DEF bool
 |- !f x y. UNCURRY f(x,y) = f x y
 \ENDTHEOREM
-\section{Theorems about disjoint sums}
+\section{Theorems about disjoint sums}\THEOREM INL\_DEF sum
+|- !e. INL e = ABS_sum(\b x y. (x = e) /\ b)
+\ENDTHEOREM
 \THEOREM INL sum
 |- !x. ISL x ==> (INL(OUTL x) = x)
 \ENDTHEOREM
-\THEOREM INL\_DEF sum
-|- !e. INL e = ABS_sum(\b x y. (x = e) /\ b)
+\THEOREM INR\_DEF sum
+|- !e. INR e = ABS_sum(\b x y. (y = e) /\ ~b)
 \ENDTHEOREM
 \THEOREM INR sum
 |- !x. ISR x ==> (INR(OUTR x) = x)
 \ENDTHEOREM
-\THEOREM INR\_DEF sum
-|- !e. INR e = ABS_sum(\b x y. (y = e) /\ ~b)
-\ENDTHEOREM
 \THEOREM ISL sum
 |- (!x. ISL(INL x)) /\ (!y. ~ISL(INR y))
 \ENDTHEOREM
@@ -433,12 +422,12 @@
 \THEOREM OUTR sum
 |- !x. OUTR(INR x) = x
 \ENDTHEOREM
-\THEOREM sum\_Axiom sum
-|- !f g. ?! h. (!x. h(INL x) = f x) /\ (!x. h(INR x) = g x)
-\ENDTHEOREM
 \THEOREM sum\_axiom sum
 |- !f g. ?! h. (h o INL = f) /\ (h o INR = g)
 \ENDTHEOREM
+\THEOREM sum\_Axiom sum
+|- !f g. ?! h. (!x. h(INL x) = f x) /\ (!x. h(INR x) = g x)
+\ENDTHEOREM
 \THEOREM sum\_ISO\_DEF sum
 |- (!a. ABS_sum(REP_sum a) = a) /\
    (!r. IS_SUM_REP r = (REP_sum(ABS_sum r) = r))
@@ -446,16 +435,12 @@
 \THEOREM sum\_TY\_DEF sum
 |- ?rep. TYPE_DEFINITION IS_SUM_REP rep
 \ENDTHEOREM
-\section{Theorems about arithmetic}
-\THEOREM ADD arithmetic
-|- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
+\section{Theorems about arithmetic}\THEOREM ADD\_0 arithmetic
+|- !m. m + 0 = m
 \ENDTHEOREM
 \THEOREM ADD1 arithmetic
 |- !m. SUC m = m + 1
 \ENDTHEOREM
-\THEOREM ADD\_0 arithmetic
-|- !m. m + 0 = m
-\ENDTHEOREM
 \THEOREM ADD\_ASSOC arithmetic
 |- !m n p. m + (n + p) = (m + n) + p
 \ENDTHEOREM
@@ -465,6 +450,9 @@
    ((SUC m) + n = SUC(m + n)) /\
    (m + (SUC n) = SUC(m + n))
 \ENDTHEOREM
+\THEOREM ADD arithmetic
+|- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
+\ENDTHEOREM
 \THEOREM ADD\_EQ\_0 arithmetic
 |- !m n. (m + n = 0) = (m = 0) /\ (n = 0)
 \ENDTHEOREM
@@ -523,15 +511,15 @@
 \THEOREM EQ\_MONO\_ADD\_EQ arithmetic
 |- !m n p. (m + p = n + p) = (m = n)
 \ENDTHEOREM
-\THEOREM EVEN arithmetic
-|- (EVEN 0 = T) /\ (!n. EVEN(SUC n) = ~EVEN n)
-\ENDTHEOREM
 \THEOREM EVEN\_ADD arithmetic
 |- !m n. EVEN(m + n) = (EVEN m = EVEN n)
 \ENDTHEOREM
 \THEOREM EVEN\_AND\_ODD arithmetic
 |- !n. ~(EVEN n /\ ODD n)
 \ENDTHEOREM
+\THEOREM EVEN arithmetic
+|- (EVEN 0 = T) /\ (!n. EVEN(SUC n) = ~EVEN n)
+\ENDTHEOREM
 \THEOREM EVEN\_DOUBLE arithmetic
 |- !n. EVEN(2 * n)
 \ENDTHEOREM
@@ -550,12 +538,12 @@
 \THEOREM EVEN\_OR\_ODD arithmetic
 |- !n. EVEN n \/ ODD n
 \ENDTHEOREM
-\THEOREM EXP arithmetic
-|- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
-\ENDTHEOREM
 \THEOREM EXP\_ADD arithmetic
 |- !p q n. n EXP (p + q) = (n EXP p) * (n EXP q)
 \ENDTHEOREM
+\THEOREM EXP arithmetic
+|- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
+\ENDTHEOREM
 \THEOREM FACT arithmetic
 |- (FACT 0 = 1) /\ (!n. FACT(SUC n) = (SUC n) * (FACT n))
 \ENDTHEOREM
@@ -609,24 +597,21 @@
 \THEOREM LEFT\_SUB\_DISTRIB arithmetic
 |- !m n p. p * (m - n) = (p * m) - (p * n)
 \ENDTHEOREM
-\THEOREM LESS prim\_rec
-|- !m n. m < n = (?P. (!n'. P(SUC n') ==> P n') /\ P m /\ ~P n)
-\ENDTHEOREM
-\THEOREM LESS\_0 prim\_rec
-|- !n. 0 < (SUC n)
-\ENDTHEOREM
 \THEOREM LESS\_0\_0 prim\_rec
 |- 0 < (SUC 0)
 \ENDTHEOREM
 \THEOREM LESS\_0\_CASES arithmetic
 |- !m. (0 = m) \/ 0 < m
 \ENDTHEOREM
-\THEOREM LESS\_ADD arithmetic
-|- !m n. n < m ==> (?p. p + n = m)
+\THEOREM LESS\_0 prim\_rec
+|- !n. 0 < (SUC n)
 \ENDTHEOREM
 \THEOREM LESS\_ADD\_1 arithmetic
 |- !m n. n < m ==> (?p. m = n + (p + 1))
 \ENDTHEOREM
+\THEOREM LESS\_ADD arithmetic
+|- !m n. n < m ==> (?p. p + n = m)
+\ENDTHEOREM
 \THEOREM LESS\_ADD\_NONZERO arithmetic
 |- !m n. ~(n = 0) ==> m < (m + n)
 \ENDTHEOREM
@@ -642,14 +627,8 @@
 \THEOREM LESS\_CASES\_IMP arithmetic
 |- !m n. ~m < n /\ ~(m = n) ==> n < m
 \ENDTHEOREM
-\THEOREM LESS\_EQ arithmetic
-|- !m n. m < n = (SUC m) <= n
-\ENDTHEOREM
-\THEOREM LESS\_EQUAL\_ADD arithmetic
-|- !m n. m <= n ==> (?p. n = m + p)
-\ENDTHEOREM
-\THEOREM LESS\_EQUAL\_ANTISYM arithmetic
-|- !n m. n <= m /\ m <= n ==> (n = m)
+\THEOREM LESS prim\_rec
+|- !m n. m < n = (?P. (!n'. P(SUC n') ==> P n') /\ P m /\ ~P n)
 \ENDTHEOREM
 \THEOREM LESS\_EQ\_0 arithmetic
 |- !n. n <= 0 = (n = 0)
@@ -666,6 +645,9 @@
 \THEOREM LESS\_EQ\_CASES arithmetic
 |- !m n. m <= n \/ n <= m
 \ENDTHEOREM
+\THEOREM LESS\_EQ arithmetic
+|- !m n. m < n = (SUC m) <= n
+\ENDTHEOREM
 \THEOREM LESS\_EQ\_EXISTS arithmetic
 |- !m n. m <= n = (?p. n = m + p)
 \ENDTHEOREM
@@ -678,12 +660,12 @@
 \THEOREM LESS\_EQ\_LESS\_TRANS arithmetic
 |- !m n p. m <= n /\ n < p ==> m < p
 \ENDTHEOREM
-\THEOREM LESS\_EQ\_MONO arithmetic
-|- !n m. (SUC n) <= (SUC m) = n <= m
-\ENDTHEOREM
 \THEOREM LESS\_EQ\_MONO\_ADD\_EQ arithmetic
 |- !m n p. (m + p) <= (n + p) = m <= n
 \ENDTHEOREM
+\THEOREM LESS\_EQ\_MONO arithmetic
+|- !n m. (SUC n) <= (SUC m) = n <= m
+\ENDTHEOREM
 \THEOREM LESS\_EQ\_REFL arithmetic
 |- !m. m <= m
 \ENDTHEOREM
@@ -696,6 +678,12 @@
 \THEOREM LESS\_EQ\_TRANS arithmetic
 |- !m n p. m <= n /\ n <= p ==> m <= p
 \ENDTHEOREM
+\THEOREM LESS\_EQUAL\_ADD arithmetic
+|- !m n. m <= n ==> (?p. n = m + p)
+\ENDTHEOREM
+\THEOREM LESS\_EQUAL\_ANTISYM arithmetic
+|- !n m. n <= m /\ m <= n ==> (n = m)
+\ENDTHEOREM
 \THEOREM LESS\_EXP\_SUC\_MONO arithmetic
 |- !n m. ((SUC(SUC m)) EXP n) < ((SUC(SUC m)) EXP (SUC n))
 \ENDTHEOREM
@@ -723,9 +711,6 @@
 \THEOREM LESS\_MOD arithmetic
 |- !n k. k < n ==> (k MOD n = k)
 \ENDTHEOREM
-\THEOREM LESS\_MONO prim\_rec
-|- !m n. m < n ==> (SUC m) < (SUC n)
-\ENDTHEOREM
 \THEOREM LESS\_MONO\_ADD arithmetic
 |- !m n p. m < n ==> (m + p) < (n + p)
 \ENDTHEOREM
@@ -735,6 +720,9 @@
 \THEOREM LESS\_MONO\_ADD\_INV arithmetic
 |- !m n p. (m + p) < (n + p) ==> m < n
 \ENDTHEOREM
+\THEOREM LESS\_MONO prim\_rec
+|- !m n. m < n ==> (SUC m) < (SUC n)
+\ENDTHEOREM
 \THEOREM LESS\_MONO\_EQ arithmetic
 |- !m n. (SUC m) < (SUC n) = m < n
 \ENDTHEOREM
@@ -759,12 +747,12 @@
 \THEOREM LESS\_OR arithmetic
 |- !m n. m < n ==> (SUC m) <= n
 \ENDTHEOREM
-\THEOREM LESS\_OR\_EQ arithmetic
-|- !m n. m <= n = m < n \/ (m = n)
-\ENDTHEOREM
 \THEOREM LESS\_OR\_EQ\_ADD arithmetic
 |- !n m. n < m \/ (?p. n = p + m)
 \ENDTHEOREM
+\THEOREM LESS\_OR\_EQ arithmetic
+|- !m n. m <= n = m < n \/ (m = n)
+\ENDTHEOREM
 \THEOREM LESS\_REFL prim\_rec
 |- !n. ~n < n
 \ENDTHEOREM
@@ -822,9 +810,6 @@
 \THEOREM MONOID\_MULT\_1 arithmetic
 |- MONOID $* 1
 \ENDTHEOREM
-\THEOREM MULT arithmetic
-|- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
-\ENDTHEOREM
 \THEOREM MULT\_0 arithmetic
 |- !m. m * 0 = 0
 \ENDTHEOREM
@@ -840,6 +825,9 @@
     ((SUC m) * n = (m * n) + n) /\
     (m * (SUC n) = m + (m * n))
 \ENDTHEOREM
+\THEOREM MULT arithmetic
+|- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
+\ENDTHEOREM
 \THEOREM MULT\_EQ\_0 arithmetic
 |- !m n. (m * n = 0) = (m = 0) \/ (n = 0)
 \ENDTHEOREM
@@ -879,12 +867,12 @@
 \THEOREM NOT\_LEQ arithmetic
 |- !m n. ~m <= n = (SUC n) <= m
 \ENDTHEOREM
-\THEOREM NOT\_LESS arithmetic
-|- !m n. ~m < n = n <= m
-\ENDTHEOREM
 \THEOREM NOT\_LESS\_0 prim\_rec
 |- !n. ~n < 0
 \ENDTHEOREM
+\THEOREM NOT\_LESS arithmetic
+|- !m n. ~m < n = n <= m
+\ENDTHEOREM
 \THEOREM NOT\_LESS\_EQ prim\_rec
 |- !m n. (m = n) ==> ~m < n
 \ENDTHEOREM
@@ -897,18 +885,18 @@
 \THEOREM NOT\_ODD\_EQ\_EVEN arithmetic
 |- !n m. ~(SUC(n + n) = m + m)
 \ENDTHEOREM
-\THEOREM NOT\_SUC num
-|- !n. ~(SUC n = 0)
-\ENDTHEOREM
 \THEOREM NOT\_SUC\_ADD\_LESS\_EQ arithmetic
 |- !m n. ~(SUC(m + n)) <= m
 \ENDTHEOREM
-\THEOREM NOT\_SUC\_LESS\_EQ arithmetic
-|- !n m. ~(SUC n) <= m = m <= n
+\THEOREM NOT\_SUC num
+|- !n. ~(SUC n = 0)
 \ENDTHEOREM
 \THEOREM NOT\_SUC\_LESS\_EQ\_0 arithmetic
 |- !n. ~(SUC n) <= 0
 \ENDTHEOREM
+\THEOREM NOT\_SUC\_LESS\_EQ arithmetic
+|- !n m. ~(SUC n) <= m = m <= n
+\ENDTHEOREM
 \THEOREM num\_Axiom prim\_rec
 |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
 \ENDTHEOREM
@@ -922,12 +910,12 @@
 \THEOREM num\_TY\_DEF num
 |- ?rep. TYPE_DEFINITION IS_NUM_REP rep
 \ENDTHEOREM
-\THEOREM ODD arithmetic
-|- (ODD 0 = F) /\ (!n. ODD(SUC n) = ~ODD n)
-\ENDTHEOREM
 \THEOREM ODD\_ADD arithmetic
 |- !m n. ODD(m + n) = ~(ODD m = ODD n)
 \ENDTHEOREM
+\THEOREM ODD arithmetic
+|- (ODD 0 = F) /\ (!n. ODD(SUC n) = ~ODD n)
+\ENDTHEOREM
 \THEOREM ODD\_DOUBLE arithmetic
 |- !n. ODD(SUC(2 * n))
 \ENDTHEOREM
@@ -946,18 +934,18 @@
 \THEOREM OR\_LESS arithmetic
 |- !m n. (SUC m) <= n ==> m < n
 \ENDTHEOREM
-\THEOREM PRE prim\_rec
-|- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
-\ENDTHEOREM
 \THEOREM PRE\_DEF prim\_rec
 |- !m. PRE m = ((m = 0) => 0 | (@n. m = SUC n))
 \ENDTHEOREM
-\THEOREM PRE\_SUB arithmetic
-|- !m n. PRE(m - n) = (PRE m) - n
+\THEOREM PRE prim\_rec
+|- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
 \ENDTHEOREM
 \THEOREM PRE\_SUB1 arithmetic
 |- !m. PRE m = m - 1
 \ENDTHEOREM
+\THEOREM PRE\_SUB arithmetic
+|- !m n. PRE(m - n) = (PRE m) - n
+\ENDTHEOREM
 \THEOREM PRE\_SUC\_EQ arithmetic
 |- !m n. 0 < n ==> ((m = PRE n) = (SUC m = n))
 \ENDTHEOREM
@@ -1013,9 +1001,6 @@
     (SIMP_REC x f 0 = x) /\
     (!m. SIMP_REC x f(SUC m) = f(SIMP_REC x f m))
 \ENDTHEOREM
-\THEOREM SUB arithmetic
-|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
-\ENDTHEOREM
 \THEOREM SUB\_0 arithmetic
 |- !m. (0 - m = 0) /\ (m - 0 = m)
 \ENDTHEOREM
@@ -1025,8 +1010,8 @@
 \THEOREM SUB\_CANCEL arithmetic
 |- !p n m. n <= p /\ m <= p ==> ((p - n = p - m) = (n = m))
 \ENDTHEOREM
-\THEOREM SUB\_EQUAL\_0 arithmetic
-|- !c. c - c = 0
+\THEOREM SUB arithmetic
+|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
 \ENDTHEOREM
 \THEOREM SUB\_EQ\_0 arithmetic
 |- !m n. (m - n = 0) = m <= n
@@ -1034,6 +1019,9 @@
 \THEOREM SUB\_EQ\_EQ\_0 arithmetic
 |- !m n. (m - n = m) = (m = 0) \/ (n = 0)
 \ENDTHEOREM
+\THEOREM SUB\_EQUAL\_0 arithmetic
+|- !c. c - c = 0
+\ENDTHEOREM
 \THEOREM SUB\_LEFT\_ADD arithmetic
 |- !m n p. m + (n - p) = (n <= p => m | (m + n) - p)
 \ENDTHEOREM
@@ -1061,12 +1049,12 @@
 \THEOREM SUB\_LESS\_0 arithmetic
 |- !n m. m < n = 0 < (n - m)
 \ENDTHEOREM
-\THEOREM SUB\_LESS\_EQ arithmetic
-|- !n m. (n - m) <= n
-\ENDTHEOREM
 \THEOREM SUB\_LESS\_EQ\_ADD arithmetic
 |- !m p. m <= p ==> (!n. (p - m) <= n = p <= (m + n))
 \ENDTHEOREM
+\THEOREM SUB\_LESS\_EQ arithmetic
+|- !n m. (n - m) <= n
+\ENDTHEOREM
 \THEOREM SUB\_LESS\_OR arithmetic
 |- !m n. n < m ==> n <= (m - 1)
 \ENDTHEOREM
@@ -1148,12 +1136,7 @@
 \THEOREM ZERO\_REP\_DEF num
 |- ZERO_REP = (@x. !y. ~(x = SUC_REP y))
 \ENDTHEOREM
-\section{Theorems about lists}
-\THEOREM ALL\_EL list
-|- (!P. ALL_EL P[] = T) /\
-   (!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
-\ENDTHEOREM
-\THEOREM ALL\_EL\_APPEND list
+\section{Theorems about lists}\THEOREM ALL\_EL\_APPEND list
 |- !P l1 l2. ALL_EL P(APPEND l1 l2) = ALL_EL P l1 /\ ALL_EL P l2
 \ENDTHEOREM
 \THEOREM ALL\_EL\_BUTFIRSTN list
@@ -1166,6 +1149,10 @@
 \THEOREM ALL\_EL\_CONJ list
 |- !P Q l. ALL_EL(\x. P x /\ Q x)l = ALL_EL P l /\ ALL_EL Q l
 \ENDTHEOREM
+\THEOREM ALL\_EL list
+|- (!P. ALL_EL P[] = T) /\
+   (!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
+\ENDTHEOREM
 \THEOREM ALL\_EL\_FIRSTN list
 |- !P l. ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(FIRSTN m l))
 \ENDTHEOREM
@@ -1214,13 +1201,12 @@
    (!h t l. AP(CONS h t)l = CONS(h(HD l))(AP t(TL l)))
 \ENDTHEOREM
 
-\THEOREM APPEND list
-|- (!l. APPEND[]l = l) /\
-   (!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
-\ENDTHEOREM
 \THEOREM APPEND\_ASSOC list
 |- !l1 l2 l3. APPEND l1(APPEND l2 l3) = APPEND(APPEND l1 l2)l3
 \ENDTHEOREM
+\THEOREM APPEND\_BUTLAST\_LAST list
+|- !l. ~(l = []) ==> (APPEND(BUTLAST l)[LAST l] = l)
+\ENDTHEOREM
 \THEOREM APPEND\_BUTLASTN\_BUTFIRSTN list
 |- !m n l.
     (m + n = LENGTH l) ==> (APPEND(BUTLASTN m l)(BUTFIRSTN n l) = l)
@@ -1228,8 +1214,9 @@
 \THEOREM APPEND\_BUTLASTN\_LASTN list
 |- !n l. n <= (LENGTH l) ==> (APPEND(BUTLASTN n l)(LASTN n l) = l)
 \ENDTHEOREM
-\THEOREM APPEND\_BUTLAST\_LAST list
-|- !l. ~(l = []) ==> (APPEND(BUTLAST l)[LAST l] = l)
+\THEOREM APPEND list
+|- (!l. APPEND[]l = l) /\
+   (!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
 \ENDTHEOREM
 \THEOREM APPEND\_FIRSTN\_BUTFIRSTN list
 |- !n l. n <= (LENGTH l) ==> (APPEND(FIRSTN n l)(BUTFIRSTN n l) = l)
@@ -1273,10 +1260,6 @@
       LEFT_ID f e ==>
       (!l. FOLDR f e(FLAT l) = FOLDR f e(MAP(FOLDR f e)l)))
 \ENDTHEOREM
-\THEOREM BUTFIRSTN list
-|- (!l. BUTFIRSTN 0 l = l) /\
-   (!n x l. BUTFIRSTN(SUC n)(CONS x l) = BUTFIRSTN n l)
-\ENDTHEOREM
 \THEOREM BUTFIRSTN\_APPEND1 list
 |- !n l1.
     n <= (LENGTH l1) ==>
@@ -1292,6 +1275,10 @@
     (n + m) <= (LENGTH l) ==>
     (BUTFIRSTN n(BUTFIRSTN m l) = BUTFIRSTN(n + m)l)
 \ENDTHEOREM
+\THEOREM BUTFIRSTN list
+|- (!l. BUTFIRSTN 0 l = l) /\
+   (!n x l. BUTFIRSTN(SUC n)(CONS x l) = BUTFIRSTN n l)
+\ENDTHEOREM
 \THEOREM BUTFIRSTN\_LASTN list
 |- !n l. n <= (LENGTH l) ==> (BUTFIRSTN n l = LASTN((LENGTH l) - n)l)
 \ENDTHEOREM
@@ -1313,13 +1300,12 @@
     n <= (LENGTH l) ==>
     (!x. BUTFIRSTN n(SNOC x l) = SNOC x(BUTFIRSTN n l))
 \ENDTHEOREM
+\THEOREM BUTLAST\_DEF list
+|- !l. BUTLAST l = SEG(PRE(LENGTH l))0 l
+\ENDTHEOREM
 \THEOREM BUTLAST list
 |- !x l. BUTLAST(SNOC x l) = l
 \ENDTHEOREM
-\THEOREM BUTLASTN list
-|- (!l. BUTLASTN 0 l = l) /\
-   (!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
-\ENDTHEOREM
 \THEOREM BUTLASTN\_1 list
 |- !l. ~(l = []) ==> (BUTLASTN 1 l = BUTLAST l)
 \ENDTHEOREM
@@ -1347,6 +1333,10 @@
     n <= (LENGTH l) ==>
     (!x. BUTLASTN n(CONS x l) = CONS x(BUTLASTN n l))
 \ENDTHEOREM
+\THEOREM BUTLASTN list
+|- (!l. BUTLASTN 0 l = l) /\
+   (!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
+\ENDTHEOREM
 \THEOREM BUTLASTN\_FIRSTN list
 |- !n l. n <= (LENGTH l) ==> (BUTLASTN n l = FIRSTN((LENGTH l) - n)l)
 \ENDTHEOREM
@@ -1381,9 +1371,6 @@
 \THEOREM BUTLASTN\_SUC\_BUTLAST list
 |- !n l. n < (LENGTH l) ==> (BUTLASTN(SUC n)l = BUTLASTN n(BUTLAST l))
 \ENDTHEOREM
-\THEOREM BUTLAST\_DEF list
-|- !l. BUTLAST l = SEG(PRE(LENGTH l))0 l
-\ENDTHEOREM
 \THEOREM COMM\_ASSOC\_FOLDL\_REVERSE list
 |- !f. COMM f ==> ASSOC f ==> (!e l. FOLDL f e(REVERSE l) = FOLDL f e l)
 \ENDTHEOREM
@@ -1400,9 +1387,6 @@
     COMM f ==>
     (!e'. MONOID f e' ==> (!e l. FOLDR f e l = f e(FOLDR f e' l)))
 \ENDTHEOREM
-\THEOREM CONS list
-|- !l. ~NULL l ==> (CONS(HD l)(TL l) = l)
-\ENDTHEOREM
 \THEOREM CONS\_11 list
 |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
 \ENDTHEOREM
@@ -1415,11 +1399,28 @@
     ABS_list
     ((\m. ((m = 0) => h | FST(REP_list t)(PRE m))),SUC(SND(REP_list t)))
 \ENDTHEOREM
+\THEOREM CONS list
+|- !l. ~NULL l ==> (CONS(HD l)(TL l) = l)
+\ENDTHEOREM
+\THEOREM EL\_APPEND1 list
+|- !n l1 l2. n < (LENGTH l1) ==> (EL n(APPEND l1 l2) = EL n l1)
+\ENDTHEOREM
+\THEOREM EL\_APPEND2 list
+|- !l1 n.
+    (LENGTH l1) <= n ==>
+    (!l2. EL n(APPEND l1 l2) = EL(n - (LENGTH l1))l2)
+\ENDTHEOREM
+\THEOREM EL\_CONS list
+|- !n. 0 < n ==> (!x l. EL n(CONS x l) = EL(PRE n)l)
+\ENDTHEOREM
 \THEOREM EL list
 |- (!l. EL 0 l = HD l) /\ (!l n. EL(SUC n)l = EL n(TL l))
 \ENDTHEOREM
-\THEOREM ELL list
-|- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))
+\THEOREM EL\_ELL list
+|- !n l. n < (LENGTH l) ==> (EL n l = ELL(PRE((LENGTH l) - n))l)
+\ENDTHEOREM
+\THEOREM EL\_IS\_EL list
+|- !n l. n < (LENGTH l) ==> IS_EL(EL n l)l
 \ENDTHEOREM
 \THEOREM ELL\_0\_SNOC list
 |- !l x. ELL 0(SNOC x l) = x
@@ -1435,9 +1436,18 @@
 \THEOREM ELL\_CONS list
 |- !n l. n < (LENGTH l) ==> (!x. ELL n(CONS x l) = ELL n l)
 \ENDTHEOREM
+\THEOREM ELL list
+|- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))
+\ENDTHEOREM
 \THEOREM ELL\_EL list
 |- !n l. n < (LENGTH l) ==> (ELL n l = EL(PRE((LENGTH l) - n))l)
 \ENDTHEOREM
+\THEOREM EL\_LENGTH\_APPEND list
+|- !l2 l1. ~NULL l2 ==> (EL(LENGTH l1)(APPEND l1 l2) = HD l2)
+\ENDTHEOREM
+\THEOREM EL\_LENGTH\_SNOC list
+|- !l x. EL(LENGTH l)(SNOC x l) = x
+\ENDTHEOREM
 \THEOREM ELL\_IS\_EL list
 |- !n l. n < (LENGTH l) ==> IS_EL(EL n l)l
 \ENDTHEOREM
@@ -1475,29 +1485,6 @@
 \THEOREM ELL\_SUC\_SNOC list
 |- !n x l. ELL(SUC n)(SNOC x l) = ELL n l
 \ENDTHEOREM
-\THEOREM EL\_APPEND1 list
-|- !n l1 l2. n < (LENGTH l1) ==> (EL n(APPEND l1 l2) = EL n l1)
-\ENDTHEOREM
-\THEOREM EL\_APPEND2 list
-|- !l1 n.
-    (LENGTH l1) <= n ==>
-    (!l2. EL n(APPEND l1 l2) = EL(n - (LENGTH l1))l2)
-\ENDTHEOREM
-\THEOREM EL\_CONS list
-|- !n. 0 < n ==> (!x l. EL n(CONS x l) = EL(PRE n)l)
-\ENDTHEOREM
-\THEOREM EL\_ELL list
-|- !n l. n < (LENGTH l) ==> (EL n l = ELL(PRE((LENGTH l) - n))l)
-\ENDTHEOREM
-\THEOREM EL\_IS\_EL list
-|- !n l. n < (LENGTH l) ==> IS_EL(EL n l)l
-\ENDTHEOREM
-\THEOREM EL\_LENGTH\_APPEND list
-|- !l2 l1. ~NULL l2 ==> (EL(LENGTH l1)(APPEND l1 l2) = HD l2)
-\ENDTHEOREM
-\THEOREM EL\_LENGTH\_SNOC list
-|- !l x. EL(LENGTH l)(SNOC x l) = x
-\ENDTHEOREM
 \THEOREM EL\_MAP list
 |- !n l. n < (LENGTH l) ==> (!f. EL n(MAP f l) = f(EL n l))
 \ENDTHEOREM
@@ -1548,17 +1535,17 @@
       LEFT_ID g e ==>
       (!l. FOLDR f e(FLAT l) = FOLDR g e(MAP(FOLDR f e)l)))
 \ENDTHEOREM
-\THEOREM FILTER list
-|- (!P. FILTER P[] = []) /\
-   (!P x l.
-     FILTER P(CONS x l) = (P x => CONS x(FILTER P l) | FILTER P l))
-\ENDTHEOREM
 \THEOREM FILTER\_APPEND list
 |- !f l1 l2. FILTER f(APPEND l1 l2) = APPEND(FILTER f l1)(FILTER f l2)
 \ENDTHEOREM
 \THEOREM FILTER\_COMM list
 |- !f1 f2 l. FILTER f1(FILTER f2 l) = FILTER f2(FILTER f1 l)
 \ENDTHEOREM
+\THEOREM FILTER list
+|- (!P. FILTER P[] = []) /\
+   (!P x l.
+     FILTER P(CONS x l) = (P x => CONS x(FILTER P l) | FILTER P l))
+\ENDTHEOREM
 \THEOREM FILTER\_FILTER list
 |- !P Q l. FILTER P(FILTER Q l) = FILTER(\x. P x /\ Q x)l
 \ENDTHEOREM
@@ -1583,10 +1570,6 @@
 \THEOREM FILTER\_SNOC list
 |- !P x l. FILTER P(SNOC x l) = (P x => SNOC x(FILTER P l) | FILTER P l)
 \ENDTHEOREM
-\THEOREM FIRSTN list
-|- (!l. FIRSTN 0 l = []) /\
-   (!n x l. FIRSTN(SUC n)(CONS x l) = CONS x(FIRSTN n l))
-\ENDTHEOREM
 \THEOREM FIRSTN\_APPEND1 list
 |- !n l1.
     n <= (LENGTH l1) ==> (!l2. FIRSTN n(APPEND l1 l2) = FIRSTN n l1)
@@ -1599,6 +1582,10 @@
 \THEOREM FIRSTN\_BUTLASTN list
 |- !n l. n <= (LENGTH l) ==> (FIRSTN n l = BUTLASTN((LENGTH l) - n)l)
 \ENDTHEOREM
+\THEOREM FIRSTN list
+|- (!l. FIRSTN 0 l = []) /\
+   (!n x l. FIRSTN(SUC n)(CONS x l) = CONS x(FIRSTN n l))
+\ENDTHEOREM
 \THEOREM FIRSTN\_FIRSTN list
 |- !m l.
     m <= (LENGTH l) ==>
@@ -1619,12 +1606,12 @@
 \THEOREM FIRSTN\_SNOC list
 |- !n l. n <= (LENGTH l) ==> (!x. FIRSTN n(SNOC x l) = FIRSTN n l)
 \ENDTHEOREM
-\THEOREM FLAT list
-|- (FLAT[] = []) /\ (!h t. FLAT(CONS h t) = APPEND h(FLAT t))
-\ENDTHEOREM
 \THEOREM FLAT\_APPEND list
 |- !l1 l2. FLAT(APPEND l1 l2) = APPEND(FLAT l1)(FLAT l2)
 \ENDTHEOREM
+\THEOREM FLAT list
+|- (FLAT[] = []) /\ (!h t. FLAT(CONS h t) = APPEND h(FLAT t))
+\ENDTHEOREM
 \THEOREM FLAT\_FLAT list
 |- !l. FLAT(FLAT l) = FLAT(MAP FLAT l)
 \ENDTHEOREM
@@ -1640,13 +1627,13 @@
 \THEOREM FLAT\_SNOC list
 |- !x l. FLAT(SNOC x l) = APPEND(FLAT l)x
 \ENDTHEOREM
+\THEOREM FOLDL\_APPEND list
+|- !f e l1 l2. FOLDL f e(APPEND l1 l2) = FOLDL f(FOLDL f e l1)l2
+\ENDTHEOREM
 \THEOREM FOLDL list
 |- (!f e. FOLDL f e[] = e) /\
    (!f e x l. FOLDL f e(CONS x l) = FOLDL f(f e x)l)
 \ENDTHEOREM
-\THEOREM FOLDL\_APPEND list
-|- !f e l1 l2. FOLDL f e(APPEND l1 l2) = FOLDL f(FOLDL f e l1)l2
-\ENDTHEOREM
 \THEOREM FOLDL\_FILTER list
 |- !f e P l. FOLDL f e(FILTER P l) = FOLDL(\x y. (P y => f x y | x))e l
 \ENDTHEOREM
@@ -1668,16 +1655,16 @@
 \THEOREM FOLDL\_SNOC\_NIL list
 |- !l. FOLDL(\xs x. SNOC x xs)[]l = l
 \ENDTHEOREM
-\THEOREM FOLDR list
-|- (!f e. FOLDR f e[] = e) /\
-   (!f e x l. FOLDR f e(CONS x l) = f x(FOLDR f e l))
-\ENDTHEOREM
 \THEOREM FOLDR\_APPEND list
 |- !f e l1 l2. FOLDR f e(APPEND l1 l2) = FOLDR f(FOLDR f e l2)l1
 \ENDTHEOREM
 \THEOREM FOLDR\_CONS\_NIL list
 |- !l. FOLDR CONS[]l = l
 \ENDTHEOREM
+\THEOREM FOLDR list
+|- (!f e. FOLDR f e[] = e) /\
+   (!f e x l. FOLDR f e(CONS x l) = f x(FOLDR f e l))
+\ENDTHEOREM
 \THEOREM FOLDR\_FILTER list
 |- !f e P l. FOLDR f e(FILTER P l) = FOLDR(\x y. (P x => f x y | y))e l
 \ENDTHEOREM
@@ -1716,10 +1703,6 @@
 \THEOREM HD list
 |- !h t. HD(CONS h t) = h
 \ENDTHEOREM
-\THEOREM IS\_EL list
-|- (!x. IS_EL x[] = F) /\
-   (!y x l. IS_EL y(CONS x l) = (y = x) \/ IS_EL y l)
-\ENDTHEOREM
 \THEOREM IS\_EL\_APPEND list
 |- !l1 l2 x. IS_EL x(APPEND l1 l2) = IS_EL x l1 \/ IS_EL x l2
 \ENDTHEOREM
@@ -1732,6 +1715,10 @@
 \THEOREM IS\_EL\_DEF list
 |- !x l. IS_EL x l = SOME_EL($= x)l
 \ENDTHEOREM
+\THEOREM IS\_EL list
+|- (!x. IS_EL x[] = F) /\
+   (!y x l. IS_EL y(CONS x l) = (y = x) \/ IS_EL y l)
+\ENDTHEOREM
 \THEOREM IS\_EL\_FILTER list
 |- !P x. P x ==> (!l. IS_EL x(FILTER P l) = IS_EL x l)
 \ENDTHEOREM
@@ -1772,15 +1759,15 @@
 \THEOREM IS\_list\_REP list
 |- !r. IS_list_REP r = (?f n. r = (\m. (m < n => f m | (@x. T))),n)
 \ENDTHEOREM
+\THEOREM IS\_PREFIX\_APPEND list
+|- !l1 l2. IS_PREFIX l1 l2 = (?l. l1 = APPEND l2 l)
+\ENDTHEOREM
 \THEOREM IS\_PREFIX list
 |- (!l. IS_PREFIX l[] = T) /\
    (!x l. IS_PREFIX[](CONS x l) = F) /\
    (!x1 l1 x2 l2.
      IS_PREFIX(CONS x1 l1)(CONS x2 l2) = (x1 = x2) /\ IS_PREFIX l1 l2)
 \ENDTHEOREM
-\THEOREM IS\_PREFIX\_APPEND list
-|- !l1 l2. IS_PREFIX l1 l2 = (?l. l1 = APPEND l2 l)
-\ENDTHEOREM
 \THEOREM IS\_PREFIX\_IS\_SUBLIST list
 |- !l1 l2. IS_PREFIX l1 l2 ==> IS_SUBLIST l1 l2
 \ENDTHEOREM
@@ -1790,6 +1777,9 @@
 \THEOREM IS\_PREFIX\_REVERSE list
 |- !l1 l2. IS_PREFIX(REVERSE l1)(REVERSE l2) = IS_SUFFIX l1 l2
 \ENDTHEOREM
+\THEOREM IS\_SUBLIST\_APPEND list
+|- !l1 l2. IS_SUBLIST l1 l2 = (?l l'. l1 = APPEND l(APPEND l2 l'))
+\ENDTHEOREM
 \THEOREM IS\_SUBLIST list
 |- (!l. IS_SUBLIST l[] = T) /\
    (!x l. IS_SUBLIST[](CONS x l) = F) /\
@@ -1797,33 +1787,32 @@
      IS_SUBLIST(CONS x1 l1)(CONS x2 l2) =
      (x1 = x2) /\ IS_PREFIX l1 l2 \/ IS_SUBLIST l1(CONS x2 l2))
 \ENDTHEOREM
-\THEOREM IS\_SUBLIST\_APPEND list
-|- !l1 l2. IS_SUBLIST l1 l2 = (?l l'. l1 = APPEND l(APPEND l2 l'))
-\ENDTHEOREM
 \THEOREM IS\_SUBLIST\_REVERSE list
 |- !l1 l2. IS_SUBLIST(REVERSE l1)(REVERSE l2) = IS_SUBLIST l1 l2
 \ENDTHEOREM
+\THEOREM IS\_SUFFIX\_APPEND list
+|- !l1 l2. IS_SUFFIX l1 l2 = (?l. l1 = APPEND l l2)
+\ENDTHEOREM
 \THEOREM IS\_SUFFIX list
 |- (!l. IS_SUFFIX l[] = T) /\
    (!x l. IS_SUFFIX[](SNOC x l) = F) /\
    (!x1 l1 x2 l2.
      IS_SUFFIX(SNOC x1 l1)(SNOC x2 l2) = (x1 = x2) /\ IS_SUFFIX l1 l2)
 \ENDTHEOREM
-\THEOREM IS\_SUFFIX\_APPEND list
-|- !l1 l2. IS_SUFFIX l1 l2 = (?l. l1 = APPEND l l2)
-\ENDTHEOREM
 \THEOREM IS\_SUFFIX\_IS\_SUBLIST list
 |- !l1 l2. IS_SUFFIX l1 l2 ==> IS_SUBLIST l1 l2
 \ENDTHEOREM
 \THEOREM IS\_SUFFIX\_REVERSE list
 |- !l1 l2. IS_SUFFIX(REVERSE l1)(REVERSE l2) = IS_PREFIX l1 l2
 \ENDTHEOREM
+\THEOREM LAST\_DEF list
+|- !l. LAST l = HD(SEG 1(PRE(LENGTH l))l)
+\ENDTHEOREM
 \THEOREM LAST list
 |- !x l. LAST(SNOC x l) = x
 \ENDTHEOREM
-\THEOREM LASTN list
-|- (!l. LASTN 0 l = []) /\
-   (!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
+\THEOREM LAST\_LASTN\_LAST list
+|- !n l. n <= (LENGTH l) ==> 0 < n ==> (LAST(LASTN n l) = LAST l)
 \ENDTHEOREM
 \THEOREM LASTN\_1 list
 |- !l. ~(l = []) ==> (LASTN 1 l = [LAST l])
@@ -1847,6 +1836,10 @@
 \THEOREM LASTN\_CONS list
 |- !n l. n <= (LENGTH l) ==> (!x. LASTN n(CONS x l) = LASTN n l)
 \ENDTHEOREM
+\THEOREM LASTN list
+|- (!l. LASTN 0 l = []) /\
+   (!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
+\ENDTHEOREM
 \THEOREM LASTN\_LASTN list
 |- !l n m.
     m <= (LENGTH l) ==> n <= m ==> (LASTN n(LASTN m l) = LASTN n l)
@@ -1866,15 +1859,6 @@
 \THEOREM LASTN\_SEG list
 |- !n l. n <= (LENGTH l) ==> (LASTN n l = SEG n((LENGTH l) - n)l)
 \ENDTHEOREM
-\THEOREM LAST\_DEF list
-|- !l. LAST l = HD(SEG 1(PRE(LENGTH l))l)
-\ENDTHEOREM
-\THEOREM LAST\_LASTN\_LAST list
-|- !n l. n <= (LENGTH l) ==> 0 < n ==> (LAST(LASTN n l) = LAST l)
-\ENDTHEOREM
-\THEOREM LENGTH list
-|- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
-\ENDTHEOREM
 \THEOREM LENGTH\_APPEND list
 |- !l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)
 \ENDTHEOREM
@@ -1891,14 +1875,17 @@
 |- !l n.
     (LENGTH l = SUC n) = (?h l'. (LENGTH l' = n) /\ (l = CONS h l'))
 \ENDTHEOREM
-\THEOREM LENGTH\_EQ list
-|- !x y. (x = y) ==> (LENGTH x = LENGTH y)
+\THEOREM LENGTH list
+|- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
 \ENDTHEOREM
 \THEOREM LENGTH\_EQ\_CONS list
 |- !P n.
     (!l. (LENGTH l = SUC n) ==> P l) =
     (!l. (LENGTH l = n) ==> (\l. !x. P(CONS x l))l)
 \ENDTHEOREM
+\THEOREM LENGTH\_EQ list
+|- !x y. (x = y) ==> (LENGTH x = LENGTH y)
+\ENDTHEOREM
 \THEOREM LENGTH\_EQ\_NIL list
 |- !P. (!l. (LENGTH l = 0) ==> P l) = P[]
 \ENDTHEOREM
@@ -1920,9 +1907,6 @@
 \THEOREM LENGTH\_LASTN list
 |- !n l. n <= (LENGTH l) ==> (LENGTH(LASTN n l) = n)
 \ENDTHEOREM
-\THEOREM LENGTH\_MAP list
-|- !l f. LENGTH(MAP f l) = LENGTH l
-\ENDTHEOREM
 \THEOREM LENGTH\_MAP2 list
 |- !l1 l2.
     (LENGTH l1 = LENGTH l2) ==>
@@ -1930,6 +1914,9 @@
       (LENGTH(MAP2 f l1 l2) = LENGTH l1) /\
       (LENGTH(MAP2 f l1 l2) = LENGTH l2))
 \ENDTHEOREM
+\THEOREM LENGTH\_MAP list
+|- !l f. LENGTH(MAP f l) = LENGTH l
+\ENDTHEOREM
 \THEOREM LENGTH\_NIL list
 |- !l. (LENGTH l = 0) = (l = [])
 \ENDTHEOREM
@@ -1984,9 +1971,6 @@
 \THEOREM list\_TY\_DEF list
 |- ?rep. TYPE_DEFINITION IS_list_REP rep
 \ENDTHEOREM
-\THEOREM MAP list
-|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
-\ENDTHEOREM
 \THEOREM MAP2 list
 |- (!f. MAP2 f[][] = []) /\
    (!f h1 t1 h2 t2.
@@ -2000,6 +1984,9 @@
 \THEOREM MAP\_APPEND list
 |- !f l1 l2. MAP f(APPEND l1 l2) = APPEND(MAP f l1)(MAP f l2)
 \ENDTHEOREM
+\THEOREM MAP list
+|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
+\ENDTHEOREM
 \THEOREM MAP\_FILTER list
 |- !f P l.
     (!x. P(f x) = P x) ==> (MAP f(FILTER P l) = FILTER P(MAP f l))
@@ -2052,12 +2039,12 @@
 \THEOREM NOT\_SOME\_EL\_ALL\_EL list
 |- !P l. ~SOME_EL P l = ALL_EL($~ o P)l
 \ENDTHEOREM
-\THEOREM NULL list
-|- NULL[] /\ (!h t. ~NULL(CONS h t))
-\ENDTHEOREM
 \THEOREM NULL\_DEF list
 |- (NULL[] = T) /\ (!h t. NULL(CONS h t) = F)
 \ENDTHEOREM
+\THEOREM NULL list
+|- NULL[] /\ (!h t. ~NULL(CONS h t))
+\ENDTHEOREM
 \THEOREM NULL\_EQ\_NIL list
 |- !l. NULL l = (l = [])
 \ENDTHEOREM
@@ -2081,13 +2068,13 @@
    (!n t l.
      PART(CONS n t)l = CONS(FST(SPLIT n l))(PART t(SND(SPLIT n l))))
 \ENDTHEOREM
+\THEOREM PREFIX\_DEF list
+|- !P l. PREFIX P l = FST(SPLITP($~ o P)l)
+\ENDTHEOREM
 \THEOREM PREFIX list
 |- (!P. PREFIX P[] = []) /\
    (!P x l. PREFIX P(CONS x l) = (P x => CONS x(PREFIX P l) | []))
 \ENDTHEOREM
-\THEOREM PREFIX\_DEF list
-|- !P l. PREFIX P l = FST(SPLITP($~ o P)l)
-\ENDTHEOREM
 \THEOREM PREFIX\_FOLDR list
 |- !P l. PREFIX P l = FOLDR(\x l'. (P x => CONS x l' | []))[]l
 \ENDTHEOREM
@@ -2095,12 +2082,12 @@
 |- (!x. REPLICATE 0 x = []) /\
    (!n x. REPLICATE(SUC n)x = CONS x(REPLICATE n x))
 \ENDTHEOREM
-\THEOREM REVERSE list
-|- (REVERSE[] = []) /\ (!x l. REVERSE(CONS x l) = SNOC x(REVERSE l))
-\ENDTHEOREM
 \THEOREM REVERSE\_APPEND list
 |- !l1 l2. REVERSE(APPEND l1 l2) = APPEND(REVERSE l2)(REVERSE l1)
 \ENDTHEOREM
+\THEOREM REVERSE list
+|- (REVERSE[] = []) /\ (!x l. REVERSE(CONS x l) = SNOC x(REVERSE l))
+\ENDTHEOREM
 \THEOREM REVERSE\_EQ\_NIL list
 |- !l. (REVERSE l = []) = (l = [])
 \ENDTHEOREM
@@ -2128,22 +2115,9 @@
    (!f e x l.
      SCANR f e(CONS x l) = CONS(f x(HD(SCANR f e l)))(SCANR f e l))
 \ENDTHEOREM
-\THEOREM SEG list
-|- (!k l. SEG 0 k l = []) /\
-   (!m x l. SEG(SUC m)0(CONS x l) = CONS x(SEG m 0 l)) /\
-   (!m k x l. SEG(SUC m)(SUC k)(CONS x l) = SEG(SUC m)k l)
-\ENDTHEOREM
 \THEOREM SEG\_0\_SNOC list
 |- !m l x. m <= (LENGTH l) ==> (SEG m 0(SNOC x l) = SEG m 0 l)
 \ENDTHEOREM
-\THEOREM SEG\_APPEND list
-|- !m l1 n l2.
-    m < (LENGTH l1) /\
-    (LENGTH l1) <= (n + m) /\
-    (n + m) <= ((LENGTH l1) + (LENGTH l2)) ==>
-    (SEG n m(APPEND l1 l2) =
-     APPEND(SEG((LENGTH l1) - m)m l1)(SEG((n + m) - (LENGTH l1))0 l2))
-\ENDTHEOREM
 \THEOREM SEG\_APPEND1 list
 |- !n m l1.
     (n + m) <= (LENGTH l1) ==> (!l2. SEG n m(APPEND l1 l2) = SEG n m l1)
@@ -2153,6 +2127,19 @@
     (LENGTH l1) <= m /\ n <= (LENGTH l2) ==>
     (SEG n m(APPEND l1 l2) = SEG n(m - (LENGTH l1))l2)
 \ENDTHEOREM
+\THEOREM SEG\_APPEND list
+|- !m l1 n l2.
+    m < (LENGTH l1) /\
+    (LENGTH l1) <= (n + m) /\
+    (n + m) <= ((LENGTH l1) + (LENGTH l2)) ==>
+    (SEG n m(APPEND l1 l2) =
+     APPEND(SEG((LENGTH l1) - m)m l1)(SEG((n + m) - (LENGTH l1))0 l2))
+\ENDTHEOREM
+\THEOREM SEG list
+|- (!k l. SEG 0 k l = []) /\
+   (!m x l. SEG(SUC m)0(CONS x l) = CONS x(SEG m 0 l)) /\
+   (!m k x l. SEG(SUC m)(SUC k)(CONS x l) = SEG(SUC m)k l)
+\ENDTHEOREM
 \THEOREM SEG\_FIRSTN\_BUTFISTN list
 |- !n m l.
     (n + m) <= (LENGTH l) ==> (SEG n m l = FIRSTN n(BUTFIRSTN m l))
@@ -2184,10 +2171,6 @@
 \THEOREM SEG\_SUC\_CONS list
 |- !m n l x. SEG m(SUC n)(CONS x l) = SEG m n l
 \ENDTHEOREM
-\THEOREM SNOC list
-|- (!x. SNOC x[] = [x]) /\
-   (!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
-\ENDTHEOREM
 \THEOREM SNOC\_11 list
 |- !x l x' l'. (SNOC x l = SNOC x' l') = (x = x') /\ (l = l')
 \ENDTHEOREM
@@ -2200,6 +2183,10 @@
 \THEOREM SNOC\_CASES list
 |- !l. (l = []) \/ (?l' x. l = SNOC x l')
 \ENDTHEOREM
+\THEOREM SNOC list
+|- (!x. SNOC x[] = [x]) /\
+   (!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
+\ENDTHEOREM
 \THEOREM SNOC\_EQ\_LENGTH\_EQ list
 |- !x1 l1 x2 l2. (SNOC x1 l1 = SNOC x2 l2) ==> (LENGTH l1 = LENGTH l2)
 \ENDTHEOREM
@@ -2212,10 +2199,6 @@
 \THEOREM SNOC\_REVERSE\_CONS list
 |- !x l. SNOC x l = REVERSE(CONS x(REVERSE l))
 \ENDTHEOREM
-\THEOREM SOME\_EL list
-|- (!P. SOME_EL P[] = F) /\
-   (!P x l. SOME_EL P(CONS x l) = P x \/ SOME_EL P l)
-\ENDTHEOREM
 \THEOREM SOME\_EL\_APPEND list
 |- !P l1 l2. SOME_EL P(APPEND l1 l2) = SOME_EL P l1 \/ SOME_EL P l2
 \ENDTHEOREM
@@ -2230,6 +2213,10 @@
 \THEOREM SOME\_EL\_DISJ list
 |- !P Q l. SOME_EL(\x. P x \/ Q x)l = SOME_EL P l \/ SOME_EL Q l
 \ENDTHEOREM
+\THEOREM SOME\_EL list
+|- (!P. SOME_EL P[] = F) /\
+   (!P x l. SOME_EL P(CONS x l) = P x \/ SOME_EL P l)
+\ENDTHEOREM
 \THEOREM SOME\_EL\_FIRSTN list
 |- !m l. m <= (LENGTH l) ==> (!P. SOME_EL P(FIRSTN m l) ==> SOME_EL P l)
 \ENDTHEOREM
@@ -2277,12 +2264,12 @@
 \THEOREM SUFFIX\_DEF list
 |- !P l. SUFFIX P l = FOLDL(\l' x. (P x => SNOC x l' | []))[]l
 \ENDTHEOREM
-\THEOREM SUM list
-|- (SUM[] = 0) /\ (!h t. SUM(CONS h t) = h + (SUM t))
-\ENDTHEOREM
 \THEOREM SUM\_APPEND list
 |- !l1 l2. SUM(APPEND l1 l2) = (SUM l1) + (SUM l2)
 \ENDTHEOREM
+\THEOREM SUM list
+|- (SUM[] = 0) /\ (!h t. SUM(CONS h t) = h + (SUM t))
+\ENDTHEOREM
 \THEOREM SUM\_FLAT list
 |- !l. SUM(FLAT l) = SUM(MAP SUM l)
 \ENDTHEOREM
@@ -2336,8 +2323,7 @@
 \THEOREM ZIP\_UNZIP list
 |- !l. ZIP(UNZIP l) = l
 \ENDTHEOREM
-\section{Theorems about trees}
-\THEOREM AP ltree
+\section{Theorems about trees}\THEOREM AP ltree
 |- (!l. AP[]l = []) /\
    (!h t l. AP(CONS h t)l = CONS(h(HD l))(AP t(TL l)))
 \ENDTHEOREM
@@ -2372,21 +2358,21 @@
 \THEOREM ltree\_TY\_DEF ltree
 |- ?rep. TYPE_DEFINITION Is_ltree rep
 \ENDTHEOREM
-\THEOREM Node ltree
-|- !v tl.
-    Node v tl =
-    ABS_ltree
-    (node(MAP(FST o REP_ltree)tl),CONS v(FLAT(MAP(SND o REP_ltree)tl)))
-\ENDTHEOREM
-\THEOREM node tree
-|- !tl. node tl = ABS_tree(node_REP(MAP REP_tree tl))
+\THEOREM node\_11 tree
+|- !tl1 tl2. (node tl1 = node tl2) = (tl1 = tl2)
 \ENDTHEOREM
 \THEOREM Node\_11 ltree
 |- !v1 v2 trl1 trl2.
     (Node v1 trl1 = Node v2 trl2) = (v1 = v2) /\ (trl1 = trl2)
 \ENDTHEOREM
-\THEOREM node\_11 tree
-|- !tl1 tl2. (node tl1 = node tl2) = (tl1 = tl2)
+\THEOREM node tree
+|- !tl. node tl = ABS_tree(node_REP(MAP REP_tree tl))
+\ENDTHEOREM
+\THEOREM Node ltree
+|- !v tl.
+    Node v tl =
+    ABS_ltree
+    (node(MAP(FST o REP_ltree)tl),CONS v(FLAT(MAP(SND o REP_ltree)tl)))
 \ENDTHEOREM
 \THEOREM Node\_onto ltree
 |- !l. ?v trl. l = Node v trl
@@ -2426,8 +2412,7 @@
     trf n f =
     (@fn. !trl. (HT(node trl)) <= n ==> (fn(node trl) = f(MAP fn trl)))
 \ENDTHEOREM
-\section{Theorems used to define types}
-\THEOREM ABS\_REP\_THM BASIC-HOL
+\section{Theorems used to define types}\THEOREM ABS\_REP\_THM BASIC-HOL
 |- !P.
     (?rep. TYPE_DEFINITION P rep) ==>
     (?rep abs. (!a. abs(rep a) = a) /\ (!r. P r = (rep(abs r) = r)))
@@ -2435,17 +2420,11 @@
 \THEOREM exists\_TRP tydefs
 |- !P. (?v. P v[]) ==> (?t. TRP P t)
 \ENDTHEOREM
-\THEOREM TRP tydefs
-|- !P v tl. TRP P(Node v tl) = P v tl /\ ALL_EL(TRP P)tl
-\ENDTHEOREM
 \THEOREM TRP\_DEF tydefs
 |- !P. TRP P = (@trp. !v tl. trp(Node v tl) = P v tl /\ ALL_EL trp tl)
 \ENDTHEOREM
-\THEOREM TYPE\_DEFINITION bool
-|- !P rep.
-    TYPE_DEFINITION P rep =
-    (!x' x''. (rep x' = rep x'') ==> (x' = x'')) /\
-    (!x. P x = (?x'. x = rep x'))
+\THEOREM TRP tydefs
+|- !P v tl. TRP P(Node v tl) = P v tl /\ ALL_EL(TRP P)tl
 \ENDTHEOREM
 \THEOREM TY\_DEF\_THM tydefs
 |- !REP ABS P.
@@ -2456,3 +2435,9 @@
         P v(MAP REP tl) ==>
         (fn(ABS(Node v(MAP REP tl))) = f(MAP fn tl)v tl))
 \ENDTHEOREM
+\THEOREM TYPE\_DEFINITION bool
+|- !P rep.
+    TYPE_DEFINITION P rep =
+    (!x' x''. (rep x' = rep x'') ==> (x' = x'')) /\
+    (!x. P x = (?x'. x = rep x'))
+\ENDTHEOREM
--- hol88-2.02.19940316.orig/Manual/Reference/index.tex
+++ hol88-2.02.19940316/Manual/Reference/index.tex
@@ -1,1625 +1,3 @@
-\begin{theindex}
-
-  \item {\ptt *}, 1
-  \item {\ptt +}, 2
-  \item {\ptt -}, 2
-  \item {\ptt /}, 3
-  \item {\ptt <}, 4
-  \item {\ptt <<}, 4
-  \item {\ptt =}, 4
-  \item {\ptt >}, 6
-  \item {\ptt \#}, 1
-  \item {\ptt \char '056}, 2
-  \item {\ptt \char '100}, 7
-  \item {\ptt \char '136}, 3
-
-  \indexspace
-
-  \item {\ptt ABS}, 7
-  \item {\ptt ABS\_CONV}, 8
-  \item {\ptt abs\_goals}, 9
-  \item {\ptt ABS\_REP\_THM}, 661
-  \item {\ptt ABS\_SIMP}, 614
-  \item {\ptt AC\_CONV}, 11
-  \item {\ptt ACCEPT\_TAC}, 9
-  \item {\ptt achieve\_first}, 10
-  \item {\ptt achieves}, 10
-  \item {\ptt aconv}, 10
-  \item {\ptt activate\_binders}, 11
-  \item {\ptt ADD}, 619
-  \item {\ptt ADD1}, 619
-  \item {\ptt ADD\_0}, 619
-  \item {\ptt ADD\_ASSOC}, 619
-  \item {\ptt ADD\_ASSUM}, 12
-  \item {\ptt ADD\_CLAUSES}, 619
-  \item {\ptt ADD\_CONV}, 13
-  \item {\ptt ADD\_EQ\_0}, 619
-  \item {\ptt ADD\_EQ\_SUB}, 619
-  \item {\ptt ADD\_INV\_0}, 619
-  \item {\ptt ADD\_INV\_0\_EQ}, 619
-  \item {\ptt ADD\_MONO\_LESS\_EQ}, 619
-  \item {\ptt ADD\_SUB}, 619
-  \item {\ptt ADD\_SUC}, 619
-  \item {\ptt ADD\_SYM}, 619
-  \item {\ptt ALL\_CONV}, 15
-  \item {\ptt ALL\_EL}, 634
-  \item {\ptt ALL\_EL\_APPEND}, 634
-  \item {\ptt ALL\_EL\_BUTFIRSTN}, 634
-  \item {\ptt ALL\_EL\_BUTLASTN}, 634
-  \item {\ptt ALL\_EL\_CONJ}, 634
-  \item {\ptt ALL\_EL\_CONV}, 15
-  \item {\ptt ALL\_EL\_FIRSTN}, 634
-  \item {\ptt ALL\_EL\_FOLDL}, 634
-  \item {\ptt ALL\_EL\_FOLDL\_MAP}, 634
-  \item {\ptt ALL\_EL\_FOLDR}, 634
-  \item {\ptt ALL\_EL\_FOLDR\_MAP}, 634
-  \item {\ptt ALL\_EL\_LASTN}, 634
-  \item {\ptt ALL\_EL\_MAP}, 634
-  \item {\ptt ALL\_EL\_REPLICATE}, 634
-  \item {\ptt ALL\_EL\_REVERSE}, 634
-  \item {\ptt ALL\_EL\_SEG}, 635
-  \item {\ptt ALL\_EL\_SNOC}, 635
-  \item {\ptt ALL\_TAC}, 16
-  \item {\ptt ALL\_THEN}, 17
-  \item {\ptt allowed\_constant}, 14
-  \item {\ptt ALPHA}, 17
-  \item {\ptt ALPHA\_CONV}, 18
-  \item {\ptt ancestors}, 19
-  \item {\ptt ancestry}, 19
-  \item {\ptt AND1\_THM}, 611
-  \item {\ptt AND2\_THM}, 611
-  \item {\ptt AND\_CLAUSES}, 611
-  \item {\ptt AND\_DEF}, 609
-  \item {\ptt AND\_EL\_DEF}, 635
-  \item {\ptt AND\_EL\_FOLDL}, 635
-  \item {\ptt AND\_EL\_FOLDR}, 635
-  \item {\ptt AND\_EXISTS\_CONV}, 20
-  \item {\ptt AND\_FORALL\_CONV}, 20
-  \item {\ptt AND\_IMP\_INTRO}, 611
-  \item {\ptt AND\_INTRO\_THM}, 611
-  \item {\ptt ANTE\_CONJ\_CONV}, 21
-  \item {\ptt ANTE\_RES\_THEN}, 21
-  \item {\ptt AP}, 635, 659
-  \item {\ptt AP\_TERM}, 25
-  \item {\ptt AP\_TERM\_TAC}, 25
-  \item {\ptt AP\_THM}, 26
-  \item {\ptt AP\_THM\_TAC}, 26
-  \item {\ptt APPEND}, 635
-  \item {\ptt append}, 22
-  \item {\ptt APPEND\_ASSOC}, 635
-  \item {\ptt APPEND\_BUTLAST\_LAST}, 635
-  \item {\ptt APPEND\_BUTLASTN\_BUTFIRSTN}, 635
-  \item {\ptt APPEND\_BUTLASTN\_LASTN}, 635
-  \item {\ptt APPEND\_CONV}, 23
-  \item {\ptt APPEND\_FIRSTN\_BUTFIRSTN}, 635
-  \item {\ptt APPEND\_FIRSTN\_LASTN}, 635
-  \item {\ptt APPEND\_FOLDL}, 635
-  \item {\ptt APPEND\_FOLDR}, 636
-  \item {\ptt APPEND\_LENGTH\_EQ}, 636
-  \item {\ptt APPEND\_NIL}, 636
-  \item {\ptt append\_openw}, 23
-  \item {\ptt APPEND\_SNOC}, 636
-  \item {\ptt apply\_proof}, 24
-  \item {\ptt ARB}, 610
-  \item {\ptt arb\_term}, 27
-  \item {\ptt ARB\_THM}, 610
-  \item {\ptt arity}, 27
-  \item {\ptt ascii}, 28
-  \item {\ptt ascii\_code}, 28
-  \item {\ptt ASM\_CASES\_TAC}, 29
-  \item {\ptt ASM\_REWRITE\_RULE}, 29
-  \item {\ptt ASM\_REWRITE\_TAC}, 30
-  \item {\ptt assert}, 31
-  \item {\ptt assignable\_print\_term}, 32
-  \item {\ptt assoc}, 34
-  \item {\ptt ASSOC\_ADD}, 619
-  \item {\ptt ASSOC\_APPEND}, 636
-  \item {\ptt ASSOC\_CONJ}, 614
-  \item {\ptt ASSOC\_DEF}, 614
-  \item {\ptt ASSOC\_DISJ}, 614
-  \item {\ptt ASSOC\_FOLDL\_FLAT}, 636
-  \item {\ptt ASSOC\_FOLDR\_FLAT}, 636
-  \item {\ptt ASSOC\_MULT}, 620
-  \item {\ptt associate\_restriction}, 34
-  \item {\ptt ASSUM\_LIST}, 38
-  \item {\ptt ASSUME}, 36
-  \item {\ptt ASSUME\_TAC}, 37
-  \item {\ptt attempt\_first}, 39
-  \item {\ptt autoload}, 39
-  \item {\ptt autoload\_theory}, 41
-  \item {\ptt axiom}, 41
-  \item {\ptt axiom\_lfn}, 43
-  \item {\ptt axiom\_msg\_lfn}, 44
-  \item {\ptt axioms}, 42
-
-  \indexspace
-
-  \item {\ptt B}, 44
-  \item {\ptt b}, 45
-  \item {\ptt backup}, 45
-  \item {\ptt backup\_limit}, 47
-  \item {\ptt backup\_list}, 50
-  \item {\ptt basic\_rewrites}, 50
-  \item {\ptt BETA\_CONV}, 52
-  \item {\ptt BETA\_RULE}, 52
-  \item {\ptt BETA\_TAC}, 53
-  \item {\ptt bht}, 659
-  \item {\ptt binders}, 54
-  \item {\ptt bndvar}, 55
-  \item {\ptt body}, 55
-  \item {\ptt BODY\_CONJUNCTS}, 55
-  \item {\ptt BOOL\_CASES\_AX}, 610
-  \item {\ptt BOOL\_CASES\_TAC}, 56
-  \item {\ptt bool\_EQ\_CONV}, 57
-  \item {\ptt BOOL\_EQ\_DISTINCT}, 611
-  \item {\ptt bool\_ty}, 58
-  \item {\ptt BUTFIRSTN}, 636
-  \item {\ptt BUTFIRSTN\_APPEND1}, 636
-  \item {\ptt BUTFIRSTN\_APPEND2}, 636
-  \item {\ptt BUTFIRSTN\_BUTFIRSTN}, 637
-  \item {\ptt BUTFIRSTN\_CONV}, 58
-  \item {\ptt BUTFIRSTN\_LASTN}, 637
-  \item {\ptt BUTFIRSTN\_LENGTH\_APPEND}, 637
-  \item {\ptt BUTFIRSTN\_LENGTH\_NIL}, 637
-  \item {\ptt BUTFIRSTN\_REVERSE}, 637
-  \item {\ptt BUTFIRSTN\_SEG}, 637
-  \item {\ptt BUTFIRSTN\_SNOC}, 637
-  \item {\ptt BUTLAST}, 637
-  \item {\ptt butlast}, 59
-  \item {\ptt BUTLAST\_CONV}, 60
-  \item {\ptt BUTLAST\_DEF}, 639
-  \item {\ptt BUTLASTN}, 637
-  \item {\ptt BUTLASTN\_1}, 637
-  \item {\ptt BUTLASTN\_APPEND1}, 637
-  \item {\ptt BUTLASTN\_APPEND2}, 637
-  \item {\ptt BUTLASTN\_BUTLAST}, 638
-  \item {\ptt BUTLASTN\_BUTLASTN}, 638
-  \item {\ptt BUTLASTN\_CONS}, 638
-  \item {\ptt BUTLASTN\_CONV}, 59
-  \item {\ptt BUTLASTN\_FIRSTN}, 638
-  \item {\ptt BUTLASTN\_LASTN}, 638
-  \item {\ptt BUTLASTN\_LASTN\_NIL}, 638
-  \item {\ptt BUTLASTN\_LENGTH\_APPEND}, 638
-  \item {\ptt BUTLASTN\_LENGTH\_CONS}, 638
-  \item {\ptt BUTLASTN\_LENGTH\_NIL}, 638
-  \item {\ptt BUTLASTN\_MAP}, 638
-  \item {\ptt BUTLASTN\_REVERSE}, 638
-  \item {\ptt BUTLASTN\_SEG}, 638
-  \item {\ptt BUTLASTN\_SUC\_BUTLAST}, 638
-
-  \indexspace
-
-  \item {\ptt C}, 60
-  \item {\ptt cached\_theories}, 61
-  \item {\ptt can}, 61
-  \item {\ptt CANCEL\_SUB}, 620
-  \item {\ptt CASES\_THENL}, 62
-  \item {\ptt CB}, 63
-  \item {\ptt CCONTR}, 63
-  \item {\ptt change\_state}, 65
-  \item {\ptt CHANGED\_CONV}, 64
-  \item {\ptt CHANGED\_TAC}, 65
-  \item {\ptt CHECK\_ASSUME\_TAC}, 65
-  \item {\ptt check\_lhs}, 66
-  \item {\ptt check\_specification}, 66
-  \item {\ptt check\_valid}, 67
-  \item {\ptt check\_varstruct}, 67
-  \item {\ptt chktac}, 67
-  \item {\ptt CHOOSE}, 68
-  \item {\ptt CHOOSE\_TAC}, 69
-  \item {\ptt CHOOSE\_THEN}, 70
-  \item {\ptt chop\_list}, 71
-  \item {\ptt close}, 72
-  \item {\ptt close\_theory}, 72
-  \item {\ptt Co}, 73
-  \item {\ptt com}, 73
-  \item {\ptt combine}, 74
-  \item {\ptt COMM\_ASSOC\_FOLDL\_REVERSE}, 639
-  \item {\ptt COMM\_ASSOC\_FOLDR\_REVERSE}, 639
-  \item {\ptt COMM\_DEF}, 615
-  \item {\ptt COMM\_MONOID\_FOLDL}, 639
-  \item {\ptt COMM\_MONOID\_FOLDR}, 639
-  \item {\ptt COMMA\_DEF}, 617
-  \item {\ptt compile}, 74
-  \item {\ptt compilef}, 76
-  \item {\ptt compilet}, 77
-  \item {\ptt compiling}, 77
-  \item {\ptt compiling\_stack}, 78
-  \item {\ptt concat}, 79
-  \item {\ptt concatl}, 79
-  \item {\ptt concl}, 80
-  \item {\ptt COND\_ABS}, 611
-  \item {\ptt COND\_CASES\_TAC}, 80
-  \item {\ptt COND\_CLAUSES}, 611
-  \item {\ptt COND\_CONV}, 82
-  \item {\ptt COND\_DEF}, 610
-  \item {\ptt COND\_EXPAND}, 611
-  \item {\ptt COND\_ID}, 611
-  \item {\ptt COND\_RAND}, 611
-  \item {\ptt COND\_RATOR}, 611
-  \item {\ptt CONJ}, 82
-  \item {\ptt CONJ\_ASSOC}, 611
-  \item {\ptt CONJ\_DISCH}, 88
-  \item {\ptt CONJ\_DISCHL}, 89
-  \item {\ptt CONJ\_LIST}, 90
-  \item {\ptt CONJ\_PAIR}, 91
-  \item {\ptt CONJ\_SET\_CONV}, 92
-  \item {\ptt CONJ\_SYM}, 612
-  \item {\ptt CONJ\_TAC}, 92
-  \item {\ptt CONJUNCT1}, 83
-  \item {\ptt CONJUNCT2}, 83
-  \item {\ptt CONJUNCTS}, 84
-  \item {\ptt conjuncts}, 84
-  \item {\ptt CONJUNCTS\_CONV}, 85
-  \item {\ptt CONJUNCTS\_THEN}, 86
-  \item {\ptt CONJUNCTS\_THEN2}, 87
-  \item {\ptt CONS}, 639
-  \item {\ptt CONS\_11}, 639
-  \item {\ptt CONS\_APPEND}, 639
-  \item {\ptt CONS\_DEF}, 639
-  \item {\ptt constants}, 93
-  \item {\ptt CONTR}, 94
-  \item {\ptt CONTR\_TAC}, 95
-  \item {\ptt CONTRAPOS}, 94
-  \item {\ptt CONTRAPOS\_CONV}, 95
-  \item {\ptt CONV\_RULE}, 96
-  \item {\ptt CONV\_TAC}, 96
-  \item {\ptt current\_theory}, 97
-  \item {\ptt curry}, 98
-  \item {\ptt CURRY\_DEF}, 617
-
-  \indexspace
-
-  \item {\ptt DA}, 620
-  \item {\ptt DE\_MORGAN\_THM}, 612
-  \item {\ptt DEF\_EXISTS\_RULE}, 108
-  \item {\ptt define\_finite\_set\_syntax}, 99
-  \item {\ptt define\_load\_lib\_function}, 100
-  \item {\ptt define\_new\_type\_bijections}, 101
-  \item {\ptt define\_set\_abstraction\_syntax}, 102
-  \item {\ptt define\_type}, 103
-  \item {\ptt definition}, 105
-  \item {\ptt definition\_lfn}, 107
-  \item {\ptt definition\_msg\_lfn}, 108
-  \item {\ptt definitions}, 106
-  \item {\ptt delete\_cache}, 109
-  \item {\ptt delete\_thm}, 110
-  \item {\ptt DEPTH\_CONV}, 111
-  \item {\ptt dest\_abs}, 112
-  \item {\ptt dest\_comb}, 113
-  \item {\ptt dest\_cond}, 113
-  \item {\ptt dest\_conj}, 114
-  \item {\ptt dest\_cons}, 114
-  \item {\ptt dest\_const}, 115
-  \item {\ptt dest\_definition}, 115
-  \item {\ptt dest\_disj}, 115
-  \item {\ptt dest\_eq}, 116
-  \item {\ptt dest\_exists}, 116
-  \item {\ptt dest\_forall}, 117
-  \item {\ptt dest\_form}, 117
-  \item {\ptt dest\_imp}, 118
-  \item {\ptt dest\_let}, 118
-  \item {\ptt dest\_list}, 119
-  \item {\ptt dest\_neg}, 119
-  \item {\ptt dest\_neg\_imp}, 120
-  \item {\ptt dest\_node}, 659
-  \item {\ptt dest\_pabs}, 121
-  \item {\ptt dest\_pair}, 121
-  \item {\ptt dest\_pred}, 122
-  \item {\ptt dest\_select}, 122
-  \item {\ptt dest\_thm}, 123
-  \item {\ptt dest\_type}, 123
-  \item {\ptt dest\_var}, 124
-  \item {\ptt dest\_vartype}, 124
-  \item {\ptt DISCARD\_TAC}, 125
-  \item {\ptt DISCH}, 126
-  \item {\ptt disch}, 126
-  \item {\ptt DISCH\_ALL}, 127
-  \item {\ptt DISCH\_TAC}, 127
-  \item {\ptt DISCH\_THEN}, 128
-  \item {\ptt DISJ1}, 129
-  \item {\ptt DISJ1\_TAC}, 130
-  \item {\ptt DISJ2}, 131
-  \item {\ptt DISJ2\_TAC}, 131
-  \item {\ptt DISJ\_ASSOC}, 612
-  \item {\ptt DISJ\_CASES}, 133
-  \item {\ptt DISJ\_CASES\_TAC}, 134
-  \item {\ptt DISJ\_CASES\_THEN}, 135
-  \item {\ptt DISJ\_CASES\_THEN2}, 136
-  \item {\ptt DISJ\_CASES\_THENL}, 138
-  \item {\ptt DISJ\_CASES\_UNION}, 139
-  \item {\ptt DISJ\_IMP}, 139
-  \item {\ptt DISJ\_SYM}, 612
-  \item {\ptt disjuncts}, 132
-  \item {\ptt distinct}, 140
-  \item {\ptt DIV\_LESS\_EQ}, 620
-  \item {\ptt DIV\_MULT}, 620
-  \item {\ptt DIV\_UNIQUE}, 620
-  \item {\ptt DIVISION}, 620
-  \item {\ptt do}, 141
-  \item {\ptt draft\_mode}, 142
-  \item {\ptt dropout}, 142
-
-  \indexspace
-
-  \item {\ptt e}, 143
-  \item {\ptt EL}, 639
-  \item {\ptt el}, 144
-  \item {\ptt EL\_APPEND1}, 641
-  \item {\ptt EL\_APPEND2}, 641
-  \item {\ptt EL\_CONS}, 641
-  \item {\ptt EL\_CONV}, 145
-  \item {\ptt EL\_ELL}, 641
-  \item {\ptt EL\_IS\_EL}, 641
-  \item {\ptt EL\_LENGTH\_APPEND}, 641
-  \item {\ptt EL\_LENGTH\_SNOC}, 641
-  \item {\ptt EL\_MAP}, 641
-  \item {\ptt EL\_PRE\_LENGTH}, 641
-  \item {\ptt EL\_REVERSE}, 641
-  \item {\ptt EL\_REVERSE\_ELL}, 641
-  \item {\ptt EL\_SEG}, 641
-  \item {\ptt EL\_SNOC}, 641
-  \item {\ptt ELL}, 639
-  \item {\ptt ELL\_0\_SNOC}, 639
-  \item {\ptt ELL\_APPEND1}, 639
-  \item {\ptt ELL\_APPEND2}, 640
-  \item {\ptt ELL\_CONS}, 640
-  \item {\ptt ELL\_CONV}, 145
-  \item {\ptt ELL\_EL}, 640
-  \item {\ptt ELL\_IS\_EL}, 640
-  \item {\ptt ELL\_LAST}, 640
-  \item {\ptt ELL\_LENGTH\_APPEND}, 640
-  \item {\ptt ELL\_LENGTH\_CONS}, 640
-  \item {\ptt ELL\_LENGTH\_SNOC}, 640
-  \item {\ptt ELL\_MAP}, 640
-  \item {\ptt ELL\_PRE\_LENGTH}, 640
-  \item {\ptt ELL\_REVERSE}, 640
-  \item {\ptt ELL\_REVERSE\_EL}, 640
-  \item {\ptt ELL\_SEG}, 640
-  \item {\ptt ELL\_SNOC}, 640
-  \item {\ptt ELL\_SUC\_SNOC}, 640
-  \item {\ptt end\_itlist}, 146
-  \item {\ptt enter\_form\_rep}, 147
-  \item {\ptt enter\_term}, 147
-  \item {\ptt enter\_term\_rep}, 147
-  \item {\ptt EQ\_CLAUSES}, 612
-  \item {\ptt EQ\_EXPAND}, 612
-  \item {\ptt EQ\_EXT}, 615
-  \item {\ptt EQ\_IMP\_RULE}, 149
-  \item {\ptt EQ\_IMP\_THM}, 612
-  \item {\ptt EQ\_LENGTH\_INDUCT\_TAC}, 150
-  \item {\ptt EQ\_LENGTH\_SNOC\_INDUCT\_TAC}, 151
-  \item {\ptt EQ\_LESS}, 620
-  \item {\ptt EQ\_LESS\_EQ}, 620
-  \item {\ptt EQ\_LIST}, 641
-  \item {\ptt EQ\_MONO\_ADD\_EQ}, 620
-  \item {\ptt EQ\_MP}, 152
-  \item {\ptt EQ\_REFL}, 612
-  \item {\ptt EQ\_SYM}, 612
-  \item {\ptt EQ\_SYM\_EQ}, 612
-  \item {\ptt EQ\_TAC}, 152
-  \item {\ptt EQ\_TRANS}, 612
-  \item {\ptt EQF\_ELIM}, 147
-  \item {\ptt EQF\_INTRO}, 148
-  \item {\ptt EQT\_ELIM}, 148
-  \item {\ptt EQT\_INTRO}, 149
-  \item {\ptt ETA\_AX}, 610
-  \item {\ptt ETA\_CONV}, 153
-  \item {\ptt EVEN}, 620
-  \item {\ptt EVEN\_ADD}, 620
-  \item {\ptt EVEN\_AND\_ODD}, 620
-  \item {\ptt EVEN\_DOUBLE}, 620
-  \item {\ptt EVEN\_EXISTS}, 620
-  \item {\ptt EVEN\_MULT}, 621
-  \item {\ptt EVEN\_ODD}, 621
-  \item {\ptt EVEN\_ODD\_EXISTS}, 621
-  \item {\ptt EVEN\_OR\_ODD}, 621
-  \item {\ptt EVERY}, 153
-  \item {\ptt EVERY\_ASSUM}, 154
-  \item {\ptt EVERY\_CONV}, 155
-  \item {\ptt EVERY\_TCL}, 155
-  \item {\ptt EXCLUDED\_MIDDLE}, 612
-  \item {\ptt EXISTENCE}, 156
-  \item {\ptt EXISTS}, 157
-  \item {\ptt exists}, 157
-  \item {\ptt EXISTS\_AND\_CONV}, 158
-  \item {\ptt EXISTS\_DEF}, 609
-  \item {\ptt EXISTS\_EQ}, 159
-  \item {\ptt EXISTS\_GREATEST\_CONV}, 159
-  \item {\ptt EXISTS\_IMP}, 160
-  \item {\ptt EXISTS\_IMP\_CONV}, 160
-  \item {\ptt EXISTS\_LEAST\_CONV}, 161
-  \item {\ptt EXISTS\_NOT\_CONV}, 162
-  \item {\ptt EXISTS\_OR\_CONV}, 162
-  \item {\ptt EXISTS\_SIMP}, 612
-  \item {\ptt EXISTS\_TAC}, 163
-  \item {\ptt exists\_TRP}, 661
-  \item {\ptt EXISTS\_UNIQUE\_CONV}, 164
-  \item {\ptt EXISTS\_UNIQUE\_DEF}, 609
-  \item {\ptt EXP}, 621
-  \item {\ptt EXP\_ADD}, 621
-  \item {\ptt expand}, 164
-  \item {\ptt expandf}, 167
-  \item {\ptt explode}, 169
-  \item {\ptt EXT}, 169
-  \item {\ptt extend\_theory}, 170
-
-  \indexspace
-
-  \item {\ptt F\_DEF}, 609
-  \item {\ptt F\_IMP}, 613
-  \item {\ptt FACT}, 621
-  \item {\ptt FACT\_LESS}, 621
-  \item {\ptt FAIL\_TAC}, 171
-  \item {\ptt FALSITY}, 612
-  \item {\ptt falsity}, 172
-  \item {\ptt fast\_arith}, 172
-  \item {\ptt FCOMM\_ASSOC}, 615
-  \item {\ptt FCOMM\_DEF}, 615
-  \item {\ptt FCOMM\_FOLDL\_APPEND}, 642
-  \item {\ptt FCOMM\_FOLDL\_FLAT}, 642
-  \item {\ptt FCOMM\_FOLDR\_APPEND}, 642
-  \item {\ptt FCOMM\_FOLDR\_FLAT}, 642
-  \item {\ptt FILTER}, 642
-  \item {\ptt filter}, 173
-  \item {\ptt FILTER\_APPEND}, 642
-  \item {\ptt FILTER\_ASM\_REWRITE\_RULE}, 174
-  \item {\ptt FILTER\_ASM\_REWRITE\_TAC}, 174
-  \item {\ptt FILTER\_COMM}, 642
-  \item {\ptt FILTER\_CONV}, 175
-  \item {\ptt FILTER\_DISCH\_TAC}, 176
-  \item {\ptt FILTER\_DISCH\_THEN}, 177
-  \item {\ptt FILTER\_FILTER}, 642
-  \item {\ptt FILTER\_FLAT}, 642
-  \item {\ptt FILTER\_FOLDL}, 642
-  \item {\ptt FILTER\_FOLDR}, 643
-  \item {\ptt FILTER\_GEN\_TAC}, 178
-  \item {\ptt FILTER\_IDEM}, 643
-  \item {\ptt FILTER\_MAP}, 643
-  \item {\ptt FILTER\_ONCE\_ASM\_REWRITE\_RULE}, 179
-  \item {\ptt FILTER\_ONCE\_ASM\_REWRITE\_TAC}, 180
-  \item {\ptt FILTER\_PURE\_ASM\_REWRITE\_RULE}, 180
-  \item {\ptt FILTER\_PURE\_ASM\_REWRITE\_TAC}, 181
-  \item {\ptt FILTER\_PURE\_ONCE\_ASM\_REWRITE\_RULE}, 182
-  \item {\ptt FILTER\_PURE\_ONCE\_ASM\_REWRITE\_TAC}, 183
-  \item {\ptt FILTER\_REVERSE}, 643
-  \item {\ptt FILTER\_SNOC}, 643
-  \item {\ptt FILTER\_STRIP\_TAC}, 183
-  \item {\ptt FILTER\_STRIP\_THEN}, 185
-  \item {\ptt find}, 186
-  \item {\ptt find\_file}, 187
-  \item {\ptt find\_match}, 187
-  \item {\ptt find\_ml\_file}, 188
-  \item {\ptt find\_term}, 189
-  \item {\ptt find\_terms}, 190
-  \item {\ptt find\_theory}, 190
-  \item {\ptt FIRST}, 191
-  \item {\ptt FIRST\_ASSUM}, 192
-  \item {\ptt FIRST\_CONV}, 193
-  \item {\ptt FIRST\_TCL}, 193
-  \item {\ptt FIRSTN}, 643
-  \item {\ptt FIRSTN\_APPEND1}, 643
-  \item {\ptt FIRSTN\_APPEND2}, 643
-  \item {\ptt FIRSTN\_BUTLASTN}, 643
-  \item {\ptt FIRSTN\_CONV}, 191
-  \item {\ptt FIRSTN\_FIRSTN}, 643
-  \item {\ptt FIRSTN\_LENGTH\_APPEND}, 643
-  \item {\ptt FIRSTN\_LENGTH\_ID}, 643
-  \item {\ptt FIRSTN\_REVERSE}, 643
-  \item {\ptt FIRSTN\_SEG}, 643
-  \item {\ptt FIRSTN\_SNOC}, 644
-  \item {\ptt flags}, 194
-  \item {\ptt FLAT}, 644
-  \item {\ptt flat}, 194
-  \item {\ptt FLAT\_APPEND}, 644
-  \item {\ptt FLAT\_CONV}, 195
-  \item {\ptt FLAT\_FLAT}, 644
-  \item {\ptt FLAT\_FOLDL}, 644
-  \item {\ptt FLAT\_FOLDR}, 644
-  \item {\ptt FLAT\_REVERSE}, 644
-  \item {\ptt FLAT\_SNOC}, 644
-  \item {\ptt FOLDL}, 644
-  \item {\ptt FOLDL\_APPEND}, 644
-  \item {\ptt FOLDL\_CONV}, 196
-  \item {\ptt FOLDL\_FILTER}, 644
-  \item {\ptt FOLDL\_FOLDR\_REVERSE}, 644
-  \item {\ptt FOLDL\_MAP}, 644
-  \item {\ptt FOLDL\_REVERSE}, 644
-  \item {\ptt FOLDL\_SINGLE}, 644
-  \item {\ptt FOLDL\_SNOC}, 645
-  \item {\ptt FOLDL\_SNOC\_NIL}, 645
-  \item {\ptt FOLDR}, 645
-  \item {\ptt FOLDR\_APPEND}, 645
-  \item {\ptt FOLDR\_CONS\_NIL}, 645
-  \item {\ptt FOLDR\_CONV}, 197
-  \item {\ptt FOLDR\_FILTER}, 645
-  \item {\ptt FOLDR\_FILTER\_REVERSE}, 645
-  \item {\ptt FOLDR\_FOLDL}, 645
-  \item {\ptt FOLDR\_FOLDL\_REVERSE}, 645
-  \item {\ptt FOLDR\_MAP}, 645
-  \item {\ptt FOLDR\_MAP\_REVERSE}, 645
-  \item {\ptt FOLDR\_REVERSE}, 645
-  \item {\ptt FOLDR\_SINGLE}, 645
-  \item {\ptt FOLDR\_SNOC}, 645
-  \item {\ptt forall}, 198
-  \item {\ptt FORALL\_AND\_CONV}, 199
-  \item {\ptt FORALL\_DEF}, 609
-  \item {\ptt FORALL\_EQ}, 199
-  \item {\ptt FORALL\_IMP\_CONV}, 200
-  \item {\ptt FORALL\_NOT\_CONV}, 201
-  \item {\ptt FORALL\_OR\_CONV}, 201
-  \item {\ptt FORALL\_SIMP}, 612
-  \item {\ptt free\_in}, 205
-  \item {\ptt frees}, 202
-  \item {\ptt freesl}, 203
-  \item {\ptt FREEZE\_THEN}, 203
-  \item {\ptt FRONT\_CONJ\_CONV}, 205
-  \item {\ptt FST}, 617
-  \item {\ptt fst}, 206
-  \item {\ptt FST\_DEF}, 617
-  \item {\ptt FUN\_EQ\_CONV}, 207
-  \item {\ptt FUN\_EQ\_LEMMA}, 615, 621
-  \item {\ptt funpow}, 206
-
-  \indexspace
-
-  \item {\ptt g}, 208
-  \item {\ptt GEN}, 209
-  \item {\ptt GEN\_ALL}, 211
-  \item {\ptt GEN\_ALPHA\_CONV}, 212
-  \item {\ptt GEN\_BETA\_CONV}, 213
-  \item {\ptt GEN\_REWRITE\_CONV}, 214
-  \item {\ptt GEN\_REWRITE\_RULE}, 215
-  \item {\ptt GEN\_REWRITE\_TAC}, 217
-  \item {\ptt GEN\_TAC}, 219
-  \item {\ptt GENL}, 210
-  \item {\ptt GENLIST}, 646
-  \item {\ptt genvar}, 210
-  \item {\ptt get\_const\_type}, 220
-  \item {\ptt get\_flag\_value}, 221
-  \item {\ptt get\_state}, 221
-  \item {\ptt get\_steps}, 222
-  \item {\ptt get\_type}, 224
-  \item {\ptt getenv}, 219
-  \item {\ptt goals}, 224
-  \item {\ptt GREATER}, 621
-  \item {\ptt GREATER\_EQ}, 621
-  \item {\ptt GREATER\_OR\_EQ}, 621
-  \item {\ptt GSPEC}, 224
-  \item {\ptt GSUBST\_TAC}, 225
-  \item {\ptt GSYM}, 226
-
-  \indexspace
-
-  \item {\ptt HALF\_MK\_ABS}, 227
-  \item {\ptt HD}, 646
-  \item {\ptt hd}, 227
-  \item {\ptt help}, 228
-  \item {\ptt help\_search\_path}, 228
-  \item {\ptt hide\_constant}, 229
-  \item {\ptt hol\_pathname}, 229
-  \item {\ptt host\_name}, 230
-  \item {\ptt HT}, 659
-  \item {\ptt hyp}, 231
-  \item {\ptt hyp\_union}, 231
-
-  \indexspace
-
-  \item {\ptt I}, 232
-  \item {\ptt I\_DEF}, 616
-  \item {\ptt I\_o\_ID}, 616
-  \item {\ptt I\_THM}, 616
-  \item {\ptt IMP\_ANTISYM\_AX}, 610
-  \item {\ptt IMP\_ANTISYM\_RULE}, 233
-  \item {\ptt IMP\_CANON}, 234
-  \item {\ptt IMP\_CLAUSES}, 613
-  \item {\ptt IMP\_CONJ}, 234
-  \item {\ptt IMP\_DISJ\_THM}, 613
-  \item {\ptt IMP\_ELIM}, 235
-  \item {\ptt IMP\_F}, 613
-  \item {\ptt IMP\_F\_EQ\_F}, 613
-  \item {\ptt IMP\_RES\_TAC}, 236
-  \item {\ptt IMP\_RES\_THEN}, 237
-  \item {\ptt IMP\_TRANS}, 238
-  \item {\ptt implode}, 232
-  \item {\ptt INDUCT}, 239
-  \item {\ptt INDUCT\_TAC}, 240
-  \item {\ptt INDUCT\_THEN}, 240
-  \item {\ptt INDUCTION}, 621
-  \item {\ptt INFINITY\_AX}, 610
-  \item {\ptt infix\_variable}, 243
-  \item {\ptt infixes}, 242
-  \item {\ptt inject\_input}, 244
-  \item {\ptt INL}, 618
-  \item {\ptt inl}, 245
-  \item {\ptt INL\_DEF}, 618
-  \item {\ptt INR}, 618
-  \item {\ptt inr}, 245
-  \item {\ptt INR\_DEF}, 618
-  \item {\ptt INST}, 246
-  \item {\ptt inst}, 247
-  \item {\ptt inst\_check}, 248
-  \item {\ptt inst\_rename\_list}, 249
-  \item {\ptt INST\_TY\_TERM}, 252
-  \item {\ptt INST\_TYPE}, 250
-  \item {\ptt inst\_type}, 251
-  \item {\ptt install}, 248
-  \item {\ptt int\_of\_string}, 254
-  \item {\ptt int\_of\_term}, 254
-  \item {\ptt interface\_map}, 252
-  \item {\ptt intersect}, 253
-  \item {\ptt INV\_PRE\_EQ}, 621
-  \item {\ptt INV\_PRE\_LESS}, 621
-  \item {\ptt INV\_PRE\_LESS\_EQ}, 621
-  \item {\ptt INV\_SUC}, 622
-  \item {\ptt INV\_SUC\_EQ}, 622
-  \item {\ptt is\_abs}, 256
-  \item {\ptt is\_alphanum}, 257
-  \item {\ptt IS\_ASSUMPTION\_OF}, 613
-  \item {\ptt is\_axiom}, 257
-  \item {\ptt is\_binder}, 258
-  \item {\ptt is\_binder\_type}, 259
-  \item {\ptt is\_comb}, 259
-  \item {\ptt is\_cond}, 260
-  \item {\ptt is\_conj}, 260
-  \item {\ptt is\_cons}, 261
-  \item {\ptt is\_const}, 261
-  \item {\ptt is\_constant}, 262
-  \item {\ptt is\_definition}, 262
-  \item {\ptt is\_disj}, 263
-  \item {\ptt IS\_EL}, 646
-  \item {\ptt IS\_EL\_APPEND}, 646
-  \item {\ptt IS\_EL\_BUTFIRSTN}, 646
-  \item {\ptt IS\_EL\_BUTLASTN}, 646
-  \item {\ptt IS\_EL\_CONV}, 263
-  \item {\ptt IS\_EL\_DEF}, 646
-  \item {\ptt IS\_EL\_FILTER}, 646
-  \item {\ptt IS\_EL\_FIRSTN}, 646
-  \item {\ptt IS\_EL\_FOLDL}, 646
-  \item {\ptt IS\_EL\_FOLDL\_MAP}, 646
-  \item {\ptt IS\_EL\_FOLDR}, 646
-  \item {\ptt IS\_EL\_FOLDR\_MAP}, 646
-  \item {\ptt IS\_EL\_LASTN}, 646
-  \item {\ptt IS\_EL\_REPLICATE}, 646
-  \item {\ptt IS\_EL\_REVERSE}, 647
-  \item {\ptt IS\_EL\_SEG}, 647
-  \item {\ptt IS\_EL\_SNOC}, 647
-  \item {\ptt IS\_EL\_SOME\_EL}, 647
-  \item {\ptt is\_eq}, 264
-  \item {\ptt is\_exists}, 264
-  \item {\ptt is\_forall}, 265
-  \item {\ptt is\_hidden}, 265
-  \item {\ptt is\_imp}, 266
-  \item {\ptt is\_infix}, 267
-  \item {\ptt is\_infix\_type}, 267
-  \item {\ptt is\_let}, 268
-  \item {\ptt is\_letter}, 269
-  \item {\ptt is\_list}, 269
-  \item {\ptt IS\_list\_REP}, 647
-  \item {\ptt Is\_ltree}, 659
-  \item {\ptt is\_ml\_curried\_infix}, 270
-  \item {\ptt is\_ml\_infix}, 270
-  \item {\ptt is\_ml\_paired\_infix}, 271
-  \item {\ptt is\_neg}, 271
-  \item {\ptt is\_neg\_imp}, 272
-  \item {\ptt IS\_NUM\_REP}, 622
-  \item {\ptt is\_pabs}, 272
-  \item {\ptt is\_pair}, 273
-  \item {\ptt IS\_PAIR\_DEF}, 617
-  \item {\ptt is\_pred}, 273
-  \item {\ptt IS\_PREFIX}, 647
-  \item {\ptt IS\_PREFIX\_APPEND}, 647
-  \item {\ptt IS\_PREFIX\_IS\_SUBLIST}, 647
-  \item {\ptt IS\_PREFIX\_PREFIX}, 647
-  \item {\ptt IS\_PREFIX\_REVERSE}, 647
-  \item {\ptt is\_recording\_proof}, 274
-  \item {\ptt is\_select}, 274
-  \item {\ptt IS\_SUBLIST}, 647
-  \item {\ptt IS\_SUBLIST\_APPEND}, 647
-  \item {\ptt IS\_SUBLIST\_REVERSE}, 647
-  \item {\ptt IS\_SUFFIX}, 648
-  \item {\ptt IS\_SUFFIX\_APPEND}, 648
-  \item {\ptt IS\_SUFFIX\_IS\_SUBLIST}, 648
-  \item {\ptt IS\_SUFFIX\_REVERSE}, 648
-  \item {\ptt IS\_SUM\_REP}, 618
-  \item {\ptt Is\_tree\_REP}, 659
-  \item {\ptt is\_type}, 275
-  \item {\ptt is\_var}, 275
-  \item {\ptt is\_vartype}, 276
-  \item {\ptt ISL}, 618
-  \item {\ptt isl}, 255
-  \item {\ptt ISL\_OR\_ISR}, 618
-  \item {\ptt ISPEC}, 255
-  \item {\ptt ISPECL}, 256
-  \item {\ptt ISR}, 618
-  \item {\ptt it}, 276
-  \item {\ptt itlist}, 277
-  \item {\ptt itlist2}, 278
-
-  \indexspace
-
-  \item {\ptt K}, 278
-  \item {\ptt K\_DEF}, 616
-  \item {\ptt K\_THM}, 616
-  \item {\ptt KI}, 279
-
-  \indexspace
-
-  \item {\ptt LAST}, 648
-  \item {\ptt last}, 279
-  \item {\ptt LAST\_CONV}, 280
-  \item {\ptt LAST\_DEF}, 649
-  \item {\ptt LAST\_LASTN\_LAST}, 649
-  \item {\ptt LASTN}, 648
-  \item {\ptt LASTN\_1}, 648
-  \item {\ptt LASTN\_APPEND1}, 648
-  \item {\ptt LASTN\_APPEND2}, 648
-  \item {\ptt LASTN\_BUTFIRSTN}, 648
-  \item {\ptt LASTN\_BUTLASTN}, 648
-  \item {\ptt LASTN\_CONS}, 648
-  \item {\ptt LASTN\_CONV}, 280
-  \item {\ptt LASTN\_LASTN}, 648
-  \item {\ptt LASTN\_LENGTH\_APPEND}, 649
-  \item {\ptt LASTN\_LENGTH\_ID}, 649
-  \item {\ptt LASTN\_MAP}, 649
-  \item {\ptt LASTN\_REVERSE}, 649
-  \item {\ptt LASTN\_SEG}, 649
-  \item {\ptt LEFT\_ADD\_DISTRIB}, 622
-  \item {\ptt LEFT\_AND\_EXISTS\_CONV}, 281
-  \item {\ptt LEFT\_AND\_FORALL\_CONV}, 281
-  \item {\ptt LEFT\_AND\_OVER\_OR}, 613
-  \item {\ptt LEFT\_ID\_ADD\_0}, 622
-  \item {\ptt LEFT\_ID\_DEF}, 615
-  \item {\ptt LEFT\_ID\_MULT\_1}, 622
-  \item {\ptt LEFT\_IMP\_EXISTS\_CONV}, 282
-  \item {\ptt LEFT\_IMP\_FORALL\_CONV}, 282
-  \item {\ptt LEFT\_OR\_EXISTS\_CONV}, 283
-  \item {\ptt LEFT\_OR\_FORALL\_CONV}, 283
-  \item {\ptt LEFT\_OR\_OVER\_AND}, 613
-  \item {\ptt LEFT\_SUB\_DISTRIB}, 622
-  \item {\ptt LENGTH}, 649
-  \item {\ptt length}, 284
-  \item {\ptt LENGTH\_APPEND}, 649
-  \item {\ptt LENGTH\_BUTFIRSTN}, 649
-  \item {\ptt LENGTH\_BUTLAST}, 649
-  \item {\ptt LENGTH\_BUTLASTN}, 649
-  \item {\ptt LENGTH\_CONS}, 649
-  \item {\ptt LENGTH\_CONV}, 284
-  \item {\ptt LENGTH\_EQ}, 649
-  \item {\ptt LENGTH\_EQ\_CONS}, 649
-  \item {\ptt LENGTH\_EQ\_NIL}, 650
-  \item {\ptt LENGTH\_FIRSTN}, 650
-  \item {\ptt LENGTH\_FLAT}, 650
-  \item {\ptt LENGTH\_FOLDL}, 650
-  \item {\ptt LENGTH\_FOLDR}, 650
-  \item {\ptt LENGTH\_GENLIST}, 650
-  \item {\ptt LENGTH\_LASTN}, 650
-  \item {\ptt LENGTH\_MAP}, 650
-  \item {\ptt LENGTH\_MAP2}, 650
-  \item {\ptt LENGTH\_NIL}, 650
-  \item {\ptt LENGTH\_NOT\_NULL}, 650
-  \item {\ptt LENGTH\_REPLICATE}, 650
-  \item {\ptt LENGTH\_REVERSE}, 650
-  \item {\ptt LENGTH\_SCANL}, 650
-  \item {\ptt LENGTH\_SCANR}, 651
-  \item {\ptt LENGTH\_SEG}, 651
-  \item {\ptt LENGTH\_SNOC}, 651
-  \item {\ptt LENGTH\_UNZIP\_FST}, 651
-  \item {\ptt LENGTH\_UNZIP\_SND}, 651
-  \item {\ptt LENGTH\_ZIP}, 651
-  \item {\ptt LESS}, 622
-  \item {\ptt LESS\_0}, 622
-  \item {\ptt LESS\_0\_0}, 622
-  \item {\ptt LESS\_0\_CASES}, 622
-  \item {\ptt LESS\_ADD}, 622
-  \item {\ptt LESS\_ADD\_1}, 622
-  \item {\ptt LESS\_ADD\_NONZERO}, 622
-  \item {\ptt LESS\_ADD\_SUC}, 622
-  \item {\ptt LESS\_ANTISYM}, 623
-  \item {\ptt LESS\_CASES}, 623
-  \item {\ptt LESS\_CASES\_IMP}, 623
-  \item {\ptt LESS\_EQ}, 623
-  \item {\ptt LESS\_EQ\_0}, 623
-  \item {\ptt LESS\_EQ\_ADD}, 623
-  \item {\ptt LESS\_EQ\_ADD\_SUB}, 623
-  \item {\ptt LESS\_EQ\_ANTISYM}, 623
-  \item {\ptt LESS\_EQ\_CASES}, 623
-  \item {\ptt LESS\_EQ\_EXISTS}, 623
-  \item {\ptt LESS\_EQ\_IMP\_LESS\_SUC}, 623
-  \item {\ptt LESS\_EQ\_LESS\_EQ\_MONO}, 623
-  \item {\ptt LESS\_EQ\_LESS\_TRANS}, 623
-  \item {\ptt LESS\_EQ\_MONO}, 623
-  \item {\ptt LESS\_EQ\_MONO\_ADD\_EQ}, 624
-  \item {\ptt LESS\_EQ\_REFL}, 624
-  \item {\ptt LESS\_EQ\_SUB\_LESS}, 624
-  \item {\ptt LESS\_EQ\_SUC\_REFL}, 624
-  \item {\ptt LESS\_EQ\_TRANS}, 624
-  \item {\ptt LESS\_EQUAL\_ADD}, 623
-  \item {\ptt LESS\_EQUAL\_ANTISYM}, 623
-  \item {\ptt LESS\_EXP\_SUC\_MONO}, 624
-  \item {\ptt LESS\_IMP\_LESS\_ADD}, 624
-  \item {\ptt LESS\_IMP\_LESS\_OR\_EQ}, 624
-  \item {\ptt LESS\_LEMMA1}, 624
-  \item {\ptt LESS\_LEMMA2}, 624
-  \item {\ptt LESS\_LESS\_CASES}, 624
-  \item {\ptt LESS\_LESS\_EQ\_TRANS}, 624
-  \item {\ptt LESS\_LESS\_SUC}, 624
-  \item {\ptt LESS\_MOD}, 624
-  \item {\ptt LESS\_MONO}, 624
-  \item {\ptt LESS\_MONO\_ADD}, 624
-  \item {\ptt LESS\_MONO\_ADD\_EQ}, 625
-  \item {\ptt LESS\_MONO\_ADD\_INV}, 625
-  \item {\ptt LESS\_MONO\_EQ}, 625
-  \item {\ptt LESS\_MONO\_MULT}, 625
-  \item {\ptt LESS\_MONO\_REV}, 625
-  \item {\ptt LESS\_MULT2}, 625
-  \item {\ptt LESS\_MULT\_MONO}, 625
-  \item {\ptt LESS\_NOT\_EQ}, 625
-  \item {\ptt LESS\_NOT\_SUC}, 625
-  \item {\ptt LESS\_OR}, 625
-  \item {\ptt LESS\_OR\_EQ}, 625
-  \item {\ptt LESS\_OR\_EQ\_ADD}, 625
-  \item {\ptt LESS\_REFL}, 625
-  \item {\ptt LESS\_SUB\_ADD\_LESS}, 625
-  \item {\ptt LESS\_SUC}, 625
-  \item {\ptt LESS\_SUC\_EQ\_COR}, 625
-  \item {\ptt LESS\_SUC\_IMP}, 626
-  \item {\ptt LESS\_SUC\_NOT}, 626
-  \item {\ptt LESS\_SUC\_REFL}, 626
-  \item {\ptt LESS\_SUC\_SUC}, 626
-  \item {\ptt LESS\_THM}, 626
-  \item {\ptt LESS\_TRANS}, 626
-  \item {\ptt let\_after}, 285
-  \item {\ptt let\_before}, 286
-  \item {\ptt let\_CONV}, 287
-  \item {\ptt LET\_DEF}, 610
-  \item {\ptt lhs}, 289
-  \item {\ptt libraries}, 290
-  \item {\ptt library\_loader}, 290
-  \item {\ptt library\_pathname}, 292
-  \item {\ptt library\_search\_path}, 293
-  \item {\ptt link}, 294
-  \item {\ptt lisp}, 294
-  \item {\ptt lisp\_dir\_pathname}, 295
-  \item {\ptt list\_Axiom}, 651
-  \item {\ptt LIST\_BETA\_CONV}, 296
-  \item {\ptt list\_CASES}, 651
-  \item {\ptt LIST\_CONJ}, 297
-  \item {\ptt list\_EQ\_CONV}, 297
-  \item {\ptt list\_FOLD\_CONV}, 298
-  \item {\ptt LIST\_INDUCT}, 299
-  \item {\ptt list\_INDUCT}, 651
-  \item {\ptt LIST\_INDUCT\_TAC}, 300
-  \item {\ptt list\_ISO\_DEF}, 651
-  \item {\ptt list\_mk\_abs}, 301
-  \item {\ptt list\_mk\_comb}, 301
-  \item {\ptt list\_mk\_conj}, 302
-  \item {\ptt list\_mk\_disj}, 303
-  \item {\ptt LIST\_MK\_EXISTS}, 304
-  \item {\ptt list\_mk\_exists}, 304
-  \item {\ptt list\_mk\_forall}, 305
-  \item {\ptt list\_mk\_imp}, 305
-  \item {\ptt list\_mk\_pair}, 306
-  \item {\ptt LIST\_MP}, 307
-  \item {\ptt LIST\_NOT\_EQ}, 651
-  \item {\ptt list\_of\_binders}, 307
-  \item {\ptt list\_TY\_DEF}, 651
-  \item {\ptt load}, 308
-  \item {\ptt load\_axiom}, 310
-  \item {\ptt load\_axioms}, 311
-  \item {\ptt load\_definition}, 312
-  \item {\ptt load\_definitions}, 313
-  \item {\ptt load\_library}, 314
-  \item {\ptt load\_theorem}, 315
-  \item {\ptt load\_theorems}, 316
-  \item {\ptt load\_theory}, 317
-  \item {\ptt loadf}, 308
-  \item {\ptt loadt}, 309
-  \item {\ptt lookup\_form\_rep}, 318
-  \item {\ptt lookup\_term}, 318
-  \item {\ptt lookup\_term\_rep}, 318
-  \item {\ptt lsp}, 319
-  \item {\ptt ltree\_Axiom}, 659
-  \item {\ptt ltree\_Induct}, 659
-  \item {\ptt ltree\_ISO\_DEF}, 659
-  \item {\ptt ltree\_TY\_DEF}, 660
-
-  \indexspace
-
-  \item {\ptt MAP}, 651
-  \item {\ptt map}, 320
-  \item {\ptt MAP2}, 651
-  \item {\ptt map2}, 320
-  \item {\ptt MAP2\_CONV}, 321
-  \item {\ptt MAP2\_ZIP}, 652
-  \item {\ptt MAP\_APPEND}, 652
-  \item {\ptt MAP\_CONV}, 323
-  \item {\ptt MAP\_EVERY}, 324
-  \item {\ptt MAP\_FILTER}, 652
-  \item {\ptt MAP\_FIRST}, 325
-  \item {\ptt MAP\_FLAT}, 652
-  \item {\ptt MAP\_FOLDL}, 652
-  \item {\ptt MAP\_FOLDR}, 652
-  \item {\ptt MAP\_MAP\_o}, 652
-  \item {\ptt MAP\_o}, 652
-  \item {\ptt MAP\_REVERSE}, 652
-  \item {\ptt MAP\_SNOC}, 652
-  \item {\ptt mapfilter}, 322
-  \item {\ptt maptok}, 322
-  \item {\ptt match}, 326
-  \item {\ptt MATCH\_ACCEPT\_TAC}, 327
-  \item {\ptt MATCH\_MP}, 328
-  \item {\ptt MATCH\_MP\_TAC}, 329
-  \item {\ptt max\_print\_depth}, 330
-  \item {\ptt mem}, 331
-  \item {\ptt merge\_nets\_rep}, 331
-  \item {\ptt merge\_term\_nets}, 332
-  \item {\ptt message}, 332
-  \item {\ptt MK\_ABS}, 333
-  \item {\ptt mk\_abs}, 333
-  \item {\ptt MK\_COMB}, 334
-  \item {\ptt mk\_comb}, 334
-  \item {\ptt mk\_cond}, 335
-  \item {\ptt mk\_conj}, 335
-  \item {\ptt mk\_cons}, 336
-  \item {\ptt mk\_const}, 336
-  \item {\ptt mk\_conv\_net}, 337
-  \item {\ptt mk\_definition}, 337
-  \item {\ptt mk\_disj}, 337
-  \item {\ptt mk\_eq}, 338
-  \item {\ptt MK\_EXISTS}, 338
-  \item {\ptt mk\_exists}, 339
-  \item {\ptt mk\_forall}, 339
-  \item {\ptt mk\_form}, 340
-  \item {\ptt mk\_imp}, 340
-  \item {\ptt mk\_let}, 340
-  \item {\ptt mk\_list}, 341
-  \item {\ptt mk\_neg}, 342
-  \item {\ptt mk\_pabs}, 342
-  \item {\ptt mk\_pair}, 342
-  \item {\ptt mk\_pp\_thm}, 343
-  \item {\ptt mk\_pred}, 343
-  \item {\ptt mk\_primed\_var}, 344
-  \item {\ptt mk\_select}, 345
-  \item {\ptt mk\_thm}, 345
-  \item {\ptt mk\_type}, 346
-  \item {\ptt mk\_var}, 347
-  \item {\ptt mk\_vartype}, 347
-  \item {\ptt ml\_curried\_infix}, 348
-  \item {\ptt ml\_dir\_pathname}, 349
-  \item {\ptt ML\_eval}, 349
-  \item {\ptt ml\_paired\_infix}, 350
-  \item {\ptt MOD\_EQ\_0}, 626
-  \item {\ptt MOD\_MOD}, 626
-  \item {\ptt MOD\_MULT}, 626
-  \item {\ptt MOD\_ONE}, 626
-  \item {\ptt MOD\_PLUS}, 626
-  \item {\ptt MOD\_TIMES}, 626
-  \item {\ptt MOD\_UNIQUE}, 626
-  \item {\ptt MONOID\_ADD\_0}, 626
-  \item {\ptt MONOID\_APPEND\_NIL}, 652
-  \item {\ptt MONOID\_CONJ\_T}, 615
-  \item {\ptt MONOID\_DEF}, 615
-  \item {\ptt MONOID\_DISJ\_F}, 615
-  \item {\ptt MONOID\_MULT\_1}, 626
-  \item {\ptt MP}, 351
-  \item {\ptt MP\_TAC}, 351
-  \item {\ptt MULT}, 626
-  \item {\ptt MULT\_0}, 627
-  \item {\ptt MULT\_ASSOC}, 627
-  \item {\ptt MULT\_CLAUSES}, 627
-  \item {\ptt MULT\_EQ\_0}, 627
-  \item {\ptt MULT\_EXP\_MONO}, 627
-  \item {\ptt MULT\_LEFT\_1}, 627
-  \item {\ptt MULT\_LESS\_EQ\_SUC}, 627
-  \item {\ptt MULT\_MONO\_EQ}, 627
-  \item {\ptt MULT\_RIGHT\_1}, 627
-  \item {\ptt MULT\_SUC}, 627
-  \item {\ptt MULT\_SUC\_EQ}, 627
-  \item {\ptt MULT\_SYM}, 627
-
-  \indexspace
-
-  \item {\ptt n\_strip\_quant}, 391
-  \item {\ptt NEG\_DISCH}, 352
-  \item {\ptt new\_alphanum}, 353
-  \item {\ptt new\_axiom}, 354
-  \item {\ptt new\_binder}, 355
-  \item {\ptt new\_binder\_definition}, 355
-  \item {\ptt new\_constant}, 357
-  \item {\ptt new\_definition}, 358
-  \item {\ptt new\_flag}, 359
-  \item {\ptt new\_gen\_definition}, 360
-  \item {\ptt new\_infix}, 361
-  \item {\ptt new\_infix\_definition}, 362
-  \item {\ptt new\_infix\_list\_rec\_definition}, 363
-  \item {\ptt new\_infix\_prim\_rec\_definition}, 365
-  \item {\ptt new\_letter}, 367
-  \item {\ptt new\_list\_rec\_definition}, 367
-  \item {\ptt new\_open\_axiom}, 369
-  \item {\ptt new\_parent}, 369
-  \item {\ptt new\_predicate}, 370
-  \item {\ptt new\_prim\_rec\_definition}, 371
-  \item {\ptt new\_recursive\_definition}, 372
-  \item {\ptt new\_special\_symbol}, 375
-  \item {\ptt new\_specification}, 376
-  \item {\ptt new\_stack}, 377
-  \item {\ptt new\_syntax\_block}, 378
-  \item {\ptt new\_theory}, 379
-  \item {\ptt new\_type}, 380
-  \item {\ptt new\_type\_abbrev}, 381
-  \item {\ptt new\_type\_definition}, 382
-  \item {\ptt NIL\_DEF}, 652
-  \item {\ptt nil\_term\_net}, 383
-  \item {\ptt NO\_CONV}, 388
-  \item {\ptt NO\_TAC}, 388
-  \item {\ptt NO\_THEN}, 388
-  \item {\ptt Node}, 660
-  \item {\ptt node}, 660
-  \item {\ptt Node\_11}, 660
-  \item {\ptt node\_11}, 660
-  \item {\ptt Node\_onto}, 660
-  \item {\ptt node\_REP}, 660
-  \item {\ptt not}, 384
-  \item {\ptt NOT\_ALL\_EL\_SOME\_EL}, 652
-  \item {\ptt NOT\_AND}, 613
-  \item {\ptt NOT\_CLAUSES}, 613
-  \item {\ptt NOT\_CONS\_NIL}, 652
-  \item {\ptt NOT\_DEF}, 609
-  \item {\ptt NOT\_ELIM}, 384
-  \item {\ptt NOT\_EQ\_LIST}, 652
-  \item {\ptt NOT\_EQ\_SYM}, 385
-  \item {\ptt NOT\_EXISTS\_CONV}, 385
-  \item {\ptt NOT\_EXP\_0}, 627
-  \item {\ptt NOT\_F}, 613
-  \item {\ptt NOT\_FORALL\_CONV}, 386
-  \item {\ptt NOT\_GREATER}, 627
-  \item {\ptt NOT\_GREATER\_EQ}, 628
-  \item {\ptt NOT\_IMP}, 613
-  \item {\ptt NOT\_INTRO}, 386
-  \item {\ptt NOT\_LEQ}, 628
-  \item {\ptt NOT\_LESS}, 628
-  \item {\ptt NOT\_LESS\_0}, 628
-  \item {\ptt NOT\_LESS\_EQ}, 628
-  \item {\ptt NOT\_LESS\_EQUAL}, 628
-  \item {\ptt NOT\_MP}, 387
-  \item {\ptt NOT\_NIL\_CONS}, 653
-  \item {\ptt NOT\_NIL\_SNOC}, 653
-  \item {\ptt NOT\_NUM\_EQ}, 628
-  \item {\ptt NOT\_ODD\_EQ\_EVEN}, 628
-  \item {\ptt NOT\_SNOC\_NIL}, 653
-  \item {\ptt NOT\_SOME\_EL\_ALL\_EL}, 653
-  \item {\ptt NOT\_SUC}, 628
-  \item {\ptt NOT\_SUC\_ADD\_LESS\_EQ}, 628
-  \item {\ptt NOT\_SUC\_LESS\_EQ}, 628
-  \item {\ptt NOT\_SUC\_LESS\_EQ\_0}, 628
-  \item {\ptt NULL}, 653
-  \item {\ptt null}, 389
-  \item {\ptt NULL\_DEF}, 653
-  \item {\ptt NULL\_EQ\_NIL}, 653
-  \item {\ptt NULL\_FOLDL}, 653
-  \item {\ptt NULL\_FOLDR}, 653
-  \item {\ptt num\_Axiom}, 628
-  \item {\ptt num\_CASES}, 628
-  \item {\ptt num\_CONV}, 389
-  \item {\ptt num\_EQ\_CONV}, 390
-  \item {\ptt num\_ISO\_DEF}, 628
-  \item {\ptt num\_TY\_DEF}, 629
-
-  \indexspace
-
-  \item {\ptt o}, 391
-  \item {\ptt o\_ASSOC}, 616
-  \item {\ptt o\_DEF}, 616
-  \item {\ptt o\_THM}, 616
-  \item {\ptt ODD}, 629
-  \item {\ptt ODD\_ADD}, 629
-  \item {\ptt ODD\_DOUBLE}, 629
-  \item {\ptt ODD\_EVEN}, 629
-  \item {\ptt ODD\_EXISTS}, 629
-  \item {\ptt ODD\_MULT}, 629
-  \item {\ptt ODD\_OR\_EVEN}, 629
-  \item {\ptt ONCE\_ASM\_REWRITE\_RULE}, 392
-  \item {\ptt ONCE\_ASM\_REWRITE\_TAC}, 392
-  \item {\ptt ONCE\_DEPTH\_CONV}, 393
-  \item {\ptt ONCE\_REW\_DEPTH\_CONV}, 397
-  \item {\ptt ONCE\_REWRITE\_CONV}, 395
-  \item {\ptt ONCE\_REWRITE\_RULE}, 395
-  \item {\ptt ONCE\_REWRITE\_TAC}, 396
-  \item {\ptt one}, 615
-  \item {\ptt one\_Axiom}, 615
-  \item {\ptt one\_axiom}, 616
-  \item {\ptt one\_DEF}, 616
-  \item {\ptt ONE\_ONE\_DEF}, 615
-  \item {\ptt one\_TY\_DEF}, 616
-  \item {\ptt ONTO\_DEF}, 615
-  \item {\ptt oo}, 399
-  \item {\ptt openi}, 399
-  \item {\ptt openw}, 399
-  \item {\ptt OR\_CLAUSES}, 613
-  \item {\ptt OR\_DEF}, 609
-  \item {\ptt OR\_EL\_DEF}, 653
-  \item {\ptt OR\_EL\_FOLDL}, 653
-  \item {\ptt OR\_EL\_FOLDR}, 653
-  \item {\ptt OR\_ELIM\_THM}, 614
-  \item {\ptt OR\_EXISTS\_CONV}, 402
-  \item {\ptt OR\_FORALL\_CONV}, 402
-  \item {\ptt OR\_IMP\_THM}, 614
-  \item {\ptt OR\_INTRO\_THM1}, 614
-  \item {\ptt OR\_INTRO\_THM2}, 614
-  \item {\ptt OR\_LESS}, 629
-  \item {\ptt ORELSE}, 400
-  \item {\ptt ORELSE\_TCL}, 401
-  \item {\ptt ORELSEC}, 401
-  \item {\ptt OUTL}, 618
-  \item {\ptt outl}, 403
-  \item {\ptt OUTR}, 618
-  \item {\ptt outr}, 403
-
-  \indexspace
-
-  \item {\ptt p}, 404
-  \item {\ptt PAIR}, 617
-  \item {\ptt pair}, 405
-  \item {\ptt PAIR\_EQ}, 617
-  \item {\ptt PAIR\_EXISTS}, 617
-  \item {\ptt PAIRED\_BETA\_CONV}, 405
-  \item {\ptt paired\_delete\_thm}, 407
-  \item {\ptt PAIRED\_ETA\_CONV}, 407
-  \item {\ptt paired\_new\_type}, 408
-  \item {\ptt paired\_theorem}, 408
-  \item {\ptt parents}, 409
-  \item {\ptt parse\_as\_binder}, 410
-  \item {\ptt PART}, 653, 660
-  \item {\ptt PART\_MATCH}, 412
-  \item {\ptt partition}, 411
-  \item {\ptt POP\_ASSUM}, 413
-  \item {\ptt POP\_ASSUM\_LIST}, 414
-  \item {\ptt pop\_proofs}, 415
-  \item {\ptt pop\_proofs\_print}, 416
-  \item {\ptt pp\_axiom}, 416
-  \item {\ptt PRE}, 629
-  \item {\ptt PRE\_DEF}, 629
-  \item {\ptt PRE\_SUB}, 629
-  \item {\ptt PRE\_SUB1}, 629
-  \item {\ptt PRE\_SUC\_EQ}, 629
-  \item {\ptt PREFIX}, 653
-  \item {\ptt PREFIX\_DEF}, 653
-  \item {\ptt PREFIX\_FOLDR}, 654
-  \item {\ptt preterm\_abs}, 416
-  \item {\ptt preterm\_antiquot}, 417
-  \item {\ptt preterm\_comb}, 418
-  \item {\ptt preterm\_const}, 419
-  \item {\ptt preterm\_to\_term}, 419
-  \item {\ptt preterm\_typed}, 420
-  \item {\ptt preterm\_var}, 421
-  \item {\ptt PRIM\_REC}, 629
-  \item {\ptt PRIM\_REC\_EQN}, 630
-  \item {\ptt PRIM\_REC\_FUN}, 630
-  \item {\ptt PRIM\_REC\_THM}, 630
-  \item {\ptt print\_all\_thm}, 422
-  \item {\ptt print\_begin}, 423
-  \item {\ptt print\_bool}, 425
-  \item {\ptt print\_break}, 425
-  \item {\ptt print\_defined\_types}, 427
-  \item {\ptt print\_end}, 427
-  \item {\ptt print\_goal}, 428
-  \item {\ptt print\_hyps}, 429
-  \item {\ptt print\_ibegin}, 429
-  \item {\ptt print\_int}, 430
-  \item {\ptt print\_list}, 431
-  \item {\ptt print\_newline}, 432
-  \item {\ptt print\_stack}, 433
-  \item {\ptt print\_state}, 433
-  \item {\ptt print\_string}, 435
-  \item {\ptt print\_subgoals}, 435
-  \item {\ptt print\_term}, 435
-  \item {\ptt print\_theory}, 436
-  \item {\ptt print\_thm}, 437
-  \item {\ptt print\_tok}, 437
-  \item {\ptt print\_type}, 438
-  \item {\ptt print\_unquoted\_term}, 439
-  \item {\ptt print\_unquoted\_type}, 439
-  \item {\ptt print\_void}, 440
-  \item {\ptt prod\_TY\_DEF}, 617
-  \item {\ptt prompt}, 441
-  \item {\ptt PROVE}, 441
-  \item {\ptt prove}, 442
-  \item {\ptt prove\_abs\_fn\_one\_one}, 442
-  \item {\ptt prove\_abs\_fn\_onto}, 443
-  \item {\ptt prove\_cases\_thm}, 443
-  \item {\ptt prove\_constructors\_distinct}, 444
-  \item {\ptt prove\_constructors\_one\_one}, 445
-  \item {\ptt PROVE\_HYP}, 446
-  \item {\ptt prove\_induction\_thm}, 447
-  \item {\ptt prove\_rec\_fn\_exists}, 448
-  \item {\ptt prove\_rep\_fn\_one\_one}, 449
-  \item {\ptt prove\_rep\_fn\_onto}, 449
-  \item {\ptt prove\_thm}, 450
-  \item {\ptt PURE\_ASM\_REWRITE\_RULE}, 451
-  \item {\ptt PURE\_ASM\_REWRITE\_TAC}, 451
-  \item {\ptt PURE\_ONCE\_ASM\_REWRITE\_RULE}, 452
-  \item {\ptt PURE\_ONCE\_ASM\_REWRITE\_TAC}, 452
-  \item {\ptt PURE\_ONCE\_REWRITE\_CONV}, 453
-  \item {\ptt PURE\_ONCE\_REWRITE\_RULE}, 454
-  \item {\ptt PURE\_ONCE\_REWRITE\_TAC}, 454
-  \item {\ptt PURE\_REWRITE\_CONV}, 455
-  \item {\ptt PURE\_REWRITE\_RULE}, 455
-  \item {\ptt PURE\_REWRITE\_TAC}, 456
-  \item {\ptt push\_fsubgoals}, 457
-  \item {\ptt push\_print}, 457
-  \item {\ptt push\_subgoals}, 458
-
-  \indexspace
-
-  \item {\ptt quit}, 458
-
-  \indexspace
-
-  \item {\ptt r}, 458
-  \item {\ptt rand}, 459
-  \item {\ptt RAND\_CONV}, 459
-  \item {\ptt rator}, 460
-  \item {\ptt RATOR\_CONV}, 460
-  \item {\ptt read}, 461
-  \item {\ptt record\_proof}, 463
-  \item {\ptt RecordStep}, 462
-  \item {\ptt REDEPTH\_CONV}, 464
-  \item {\ptt REFL}, 466
-  \item {\ptt REFL\_CLAUSE}, 614
-  \item {\ptt REFL\_TAC}, 466
-  \item {\ptt remove}, 467
-  \item {\ptt remove\_sticky\_type}, 467
-  \item {\ptt rep\_goals}, 470
-  \item {\ptt REP\_prod}, 617
-  \item {\ptt REPEAT}, 468
-  \item {\ptt REPEAT\_GTCL}, 469
-  \item {\ptt REPEAT\_TCL}, 469
-  \item {\ptt REPEATC}, 468
-  \item {\ptt REPLICATE}, 654
-  \item {\ptt replicate}, 470
-  \item {\ptt RES\_ABSTRACT}, 610
-  \item {\ptt RES\_CANON}, 471
-  \item {\ptt RES\_EXISTS}, 610
-  \item {\ptt RES\_FORALL}, 610
-  \item {\ptt RES\_SELECT}, 610
-  \item {\ptt RES\_TAC}, 474
-  \item {\ptt RES\_THEN}, 475
-  \item {\ptt resume\_recording}, 471
-  \item {\ptt rev}, 477
-  \item {\ptt rev\_assoc}, 478
-  \item {\ptt rev\_itlist}, 478
-  \item {\ptt REVERSE}, 654
-  \item {\ptt REVERSE\_APPEND}, 654
-  \item {\ptt REVERSE\_CONV}, 477
-  \item {\ptt REVERSE\_EQ\_NIL}, 654
-  \item {\ptt REVERSE\_FLAT}, 654
-  \item {\ptt REVERSE\_FOLDL}, 654
-  \item {\ptt REVERSE\_FOLDR}, 654
-  \item {\ptt REVERSE\_REVERSE}, 654
-  \item {\ptt REVERSE\_SNOC}, 654
-  \item {\ptt REW\_DEPTH\_CONV}, 485
-  \item {\ptt REWR\_CONV}, 482
-  \item {\ptt REWRITE\_CONV}, 479
-  \item {\ptt REWRITE\_RULE}, 480
-  \item {\ptt REWRITE\_TAC}, 481
-  \item {\ptt rhs}, 487
-  \item {\ptt RIGHT\_ADD\_DISTRIB}, 630
-  \item {\ptt RIGHT\_AND\_EXISTS\_CONV}, 487
-  \item {\ptt RIGHT\_AND\_FORALL\_CONV}, 488
-  \item {\ptt RIGHT\_AND\_OVER\_OR}, 614
-  \item {\ptt RIGHT\_BETA}, 488
-  \item {\ptt RIGHT\_CONV\_RULE}, 489
-  \item {\ptt RIGHT\_ID\_ADD\_0}, 630
-  \item {\ptt RIGHT\_ID\_DEF}, 615
-  \item {\ptt RIGHT\_ID\_MULT\_1}, 630
-  \item {\ptt RIGHT\_IMP\_EXISTS\_CONV}, 490
-  \item {\ptt RIGHT\_IMP\_FORALL\_CONV}, 490
-  \item {\ptt RIGHT\_LIST\_BETA}, 491
-  \item {\ptt RIGHT\_OR\_EXISTS\_CONV}, 491
-  \item {\ptt RIGHT\_OR\_FORALL\_CONV}, 492
-  \item {\ptt RIGHT\_OR\_OVER\_AND}, 614
-  \item {\ptt RIGHT\_SUB\_DISTRIB}, 630
-  \item {\ptt root\_goal}, 492
-  \item {\ptt rotate}, 493
-  \item {\ptt rotate\_goals}, 494
-  \item {\ptt rotate\_top}, 495
-  \item {\ptt RULE\_ASSUM\_TAC}, 495
-
-  \indexspace
-
-  \item {\ptt S}, 496
-  \item {\ptt S\_DEF}, 616
-  \item {\ptt S\_THM}, 616
-  \item {\ptt save}, 496
-  \item {\ptt save\_thm}, 497
-  \item {\ptt save\_top\_thm}, 498
-  \item {\ptt SCANL}, 654
-  \item {\ptt SCANL\_CONV}, 499
-  \item {\ptt SCANR}, 654
-  \item {\ptt SCANR\_CONV}, 500
-  \item {\ptt search\_path}, 501
-  \item {\ptt SEG}, 654
-  \item {\ptt SEG\_0\_SNOC}, 654
-  \item {\ptt SEG\_APPEND}, 655
-  \item {\ptt SEG\_APPEND1}, 655
-  \item {\ptt SEG\_APPEND2}, 655
-  \item {\ptt SEG\_CONV}, 502
-  \item {\ptt SEG\_FIRSTN\_BUTFISTN}, 655
-  \item {\ptt SEG\_LASTN\_BUTLASTN}, 655
-  \item {\ptt SEG\_LENGTH\_ID}, 655
-  \item {\ptt SEG\_LENGTH\_SNOC}, 655
-  \item {\ptt SEG\_REVERSE}, 655
-  \item {\ptt SEG\_SEG}, 655
-  \item {\ptt SEG\_SNOC}, 655
-  \item {\ptt SEG\_SUC\_CONS}, 655
-  \item {\ptt SELECT\_AX}, 610
-  \item {\ptt SELECT\_CONV}, 503
-  \item {\ptt SELECT\_ELIM}, 504
-  \item {\ptt SELECT\_EQ}, 505
-  \item {\ptt SELECT\_INTRO}, 506
-  \item {\ptt SELECT\_REFL}, 614
-  \item {\ptt SELECT\_RULE}, 507
-  \item {\ptt SELECT\_UNIQUE}, 614
-  \item {\ptt set\_equal}, 509
-  \item {\ptt set\_fail}, 509
-  \item {\ptt set\_fail\_prefix}, 510
-  \item {\ptt set\_flag}, 511
-  \item {\ptt set\_goal}, 512
-  \item {\ptt set\_help}, 513
-  \item {\ptt set\_help\_search\_path}, 514
-  \item {\ptt set\_interface\_map}, 514
-  \item {\ptt set\_lambda}, 515
-  \item {\ptt set\_library\_search\_path}, 516
-  \item {\ptt set\_margin}, 517
-  \item {\ptt set\_pretty\_mode}, 517
-  \item {\ptt set\_prompt}, 518
-  \item {\ptt set\_search\_path}, 519
-  \item {\ptt set\_state}, 520
-  \item {\ptt set\_sticky\_type}, 521
-  \item {\ptt set\_string\_escape}, 522
-  \item {\ptt set\_thm\_count}, 523
-  \item {\ptt set\_turnstile}, 523
-  \item {\ptt setify}, 508
-  \item {\ptt show\_types}, 524
-  \item {\ptt SIMP\_REC}, 630
-  \item {\ptt SIMP\_REC\_EXISTS}, 630
-  \item {\ptt SIMP\_REC\_FUN}, 630
-  \item {\ptt SIMP\_REC\_FUN\_LEMMA}, 630
-  \item {\ptt SIMP\_REC\_REL}, 630
-  \item {\ptt SIMP\_REC\_THM}, 631
-  \item {\ptt Size}, 660
-  \item {\ptt SKOLEM\_CONV}, 525
-  \item {\ptt SND}, 617
-  \item {\ptt snd}, 526
-  \item {\ptt SND\_DEF}, 617
-  \item {\ptt SNOC}, 656
-  \item {\ptt SNOC\_11}, 656
-  \item {\ptt SNOC\_APPEND}, 656
-  \item {\ptt SNOC\_Axiom}, 656
-  \item {\ptt SNOC\_CASES}, 656
-  \item {\ptt SNOC\_CONV}, 526
-  \item {\ptt SNOC\_EQ\_LENGTH\_EQ}, 656
-  \item {\ptt SNOC\_FOLDR}, 656
-  \item {\ptt SNOC\_INDUCT}, 656
-  \item {\ptt SNOC\_INDUCT\_TAC}, 527
-  \item {\ptt SNOC\_REVERSE\_CONS}, 656
-  \item {\ptt SOME\_EL}, 656
-  \item {\ptt SOME\_EL\_APPEND}, 656
-  \item {\ptt SOME\_EL\_BUTFIRSTN}, 656
-  \item {\ptt SOME\_EL\_BUTLASTN}, 656
-  \item {\ptt SOME\_EL\_CONV}, 528
-  \item {\ptt SOME\_EL\_DISJ}, 656
-  \item {\ptt SOME\_EL\_FIRSTN}, 657
-  \item {\ptt SOME\_EL\_FOLDL}, 657
-  \item {\ptt SOME\_EL\_FOLDL\_MAP}, 657
-  \item {\ptt SOME\_EL\_FOLDR}, 657
-  \item {\ptt SOME\_EL\_FOLDR\_MAP}, 657
-  \item {\ptt SOME\_EL\_LASTN}, 657
-  \item {\ptt SOME\_EL\_MAP}, 657
-  \item {\ptt SOME\_EL\_REVERSE}, 657
-  \item {\ptt SOME\_EL\_SEG}, 657
-  \item {\ptt SOME\_EL\_SNOC}, 657
-  \item {\ptt sort}, 529
-  \item {\ptt SPEC}, 530
-  \item {\ptt SPEC\_ALL}, 532
-  \item {\ptt SPEC\_TAC}, 533
-  \item {\ptt SPEC\_VAR}, 534
-  \item {\ptt special\_symbols}, 531
-  \item {\ptt SPECL}, 531
-  \item {\ptt SPLIT}, 657, 660
-  \item {\ptt split}, 534
-  \item {\ptt SPLITP}, 657
-  \item {\ptt splitp}, 535
-  \item {\ptt sticky\_list}, 535
-  \item {\ptt store\_binders}, 536
-  \item {\ptt store\_definition}, 536
-  \item {\ptt string\_of\_int}, 536
-  \item {\ptt strip\_abs}, 537
-  \item {\ptt STRIP\_ASSUME\_TAC}, 537
-  \item {\ptt strip\_comb}, 539
-  \item {\ptt strip\_exists}, 540
-  \item {\ptt strip\_forall}, 540
-  \item {\ptt STRIP\_GOAL\_THEN}, 541
-  \item {\ptt strip\_imp}, 543
-  \item {\ptt strip\_pair}, 543
-  \item {\ptt STRIP\_TAC}, 544
-  \item {\ptt STRIP\_THM\_THEN}, 545
-  \item {\ptt STRUCT\_CASES\_TAC}, 547
-  \item {\ptt SUB}, 631
-  \item {\ptt SUB\_0}, 631
-  \item {\ptt SUB\_ADD}, 631
-  \item {\ptt SUB\_CANCEL}, 631
-  \item {\ptt SUB\_CONV}, 563
-  \item {\ptt SUB\_EQ\_0}, 631
-  \item {\ptt SUB\_EQ\_EQ\_0}, 631
-  \item {\ptt SUB\_EQUAL\_0}, 631
-  \item {\ptt SUB\_LEFT\_ADD}, 631
-  \item {\ptt SUB\_LEFT\_EQ}, 631
-  \item {\ptt SUB\_LEFT\_GREATER}, 631
-  \item {\ptt SUB\_LEFT\_GREATER\_EQ}, 631
-  \item {\ptt SUB\_LEFT\_LESS}, 631
-  \item {\ptt SUB\_LEFT\_LESS\_EQ}, 631
-  \item {\ptt SUB\_LEFT\_SUB}, 631
-  \item {\ptt SUB\_LEFT\_SUC}, 632
-  \item {\ptt SUB\_LESS\_0}, 632
-  \item {\ptt SUB\_LESS\_EQ}, 632
-  \item {\ptt SUB\_LESS\_EQ\_ADD}, 632
-  \item {\ptt SUB\_LESS\_OR}, 632
-  \item {\ptt SUB\_MONO\_EQ}, 632
-  \item {\ptt SUB\_PLUS}, 632
-  \item {\ptt SUB\_RIGHT\_ADD}, 632
-  \item {\ptt SUB\_RIGHT\_EQ}, 632
-  \item {\ptt SUB\_RIGHT\_GREATER}, 632
-  \item {\ptt SUB\_RIGHT\_GREATER\_EQ}, 632
-  \item {\ptt SUB\_RIGHT\_LESS}, 632
-  \item {\ptt SUB\_RIGHT\_LESS\_EQ}, 632
-  \item {\ptt SUB\_RIGHT\_SUB}, 632
-  \item {\ptt SUB\_SUB}, 632
-  \item {\ptt SUBGOAL\_THEN}, 548
-  \item {\ptt SUBS}, 549
-  \item {\ptt SUBS\_OCCS}, 561
-  \item {\ptt SUBST}, 551
-  \item {\ptt subst}, 552
-  \item {\ptt SUBST1\_TAC}, 553
-  \item {\ptt SUBST\_ALL\_TAC}, 554
-  \item {\ptt SUBST\_CONV}, 555
-  \item {\ptt SUBST\_MATCH}, 557
-  \item {\ptt subst\_occs}, 558
-  \item {\ptt SUBST\_OCCS\_TAC}, 559
-  \item {\ptt SUBST\_TAC}, 560
-  \item {\ptt subtract}, 562
-  \item {\ptt SUC\_ADD\_SYM}, 632
-  \item {\ptt SUC\_DEF}, 633
-  \item {\ptt SUC\_ID}, 633
-  \item {\ptt SUC\_LESS}, 633
-  \item {\ptt SUC\_NOT}, 633
-  \item {\ptt SUC\_ONE\_ADD}, 633
-  \item {\ptt SUC\_REP\_DEF}, 633
-  \item {\ptt SUC\_SUB1}, 633
-  \item {\ptt SUFFIX\_DEF}, 657
-  \item {\ptt SUM}, 658
-  \item {\ptt SUM\_APPEND}, 658
-  \item {\ptt sum\_Axiom}, 618
-  \item {\ptt sum\_axiom}, 618
-  \item {\ptt SUM\_FLAT}, 658
-  \item {\ptt SUM\_FOLDL}, 658
-  \item {\ptt SUM\_FOLDR}, 658
-  \item {\ptt sum\_ISO\_DEF}, 618
-  \item {\ptt SUM\_REVERSE}, 658
-  \item {\ptt SUM\_SNOC}, 658
-  \item {\ptt sum\_TY\_DEF}, 618
-  \item {\ptt suspend\_recording}, 564
-  \item {\ptt SWAP\_EXISTS\_CONV}, 565
-  \item {\ptt SYM}, 565
-  \item {\ptt SYM\_CONV}, 566
-  \item {\ptt syserror}, 566
-  \item {\ptt system}, 567
-
-  \indexspace
-
-  \item {\ptt T\_DEF}, 609
-  \item {\ptt TAC\_PROOF}, 567
-  \item {\ptt term\_of\_int}, 568
-  \item {\ptt THEN}, 568
-  \item {\ptt THEN\_TCL}, 570
-  \item {\ptt THENC}, 569
-  \item {\ptt THENL}, 570
-  \item {\ptt theorem}, 571
-  \item {\ptt theorem\_lfn}, 573
-  \item {\ptt theorem\_msg\_lfn}, 573
-  \item {\ptt theorems}, 572
-  \item {\ptt thm\_count}, 574
-  \item {\ptt thm\_frees}, 575
-  \item {\ptt timer}, 575
-  \item {\ptt TIMES2}, 633
-  \item {\ptt TL}, 658
-  \item {\ptt tl}, 576
-  \item {\ptt TL\_SNOC}, 658
-  \item {\ptt TOP\_DEPTH\_CONV}, 577
-  \item {\ptt top\_goal}, 578
-  \item {\ptt top\_print}, 578
-  \item {\ptt top\_proof}, 579
-  \item {\ptt top\_thm}, 580
-  \item {\ptt TRANS}, 580
-  \item {\ptt tree\_Axiom}, 660
-  \item {\ptt tree\_Induct}, 660
-  \item {\ptt tree\_ISO\_DEF}, 661
-  \item {\ptt tree\_TY\_DEF}, 661
-  \item {\ptt trf}, 661
-  \item {\ptt TRP}, 661
-  \item {\ptt TRP\_DEF}, 661
-  \item {\ptt TRUTH}, 614
-  \item {\ptt TRY}, 581
-  \item {\ptt TRY\_CONV}, 582
-  \item {\ptt tryfind}, 582
-  \item {\ptt tty\_read}, 583
-  \item {\ptt tty\_write}, 583
-  \item {\ptt TY\_DEF\_THM}, 661
-  \item {\ptt type\_abbrevs}, 585
-  \item {\ptt TYPE\_DEFINITION}, 661
-  \item {\ptt type\_in}, 586
-  \item {\ptt type\_in\_type}, 587
-  \item {\ptt type\_of}, 587
-  \item {\ptt type\_tyvars}, 588
-  \item {\ptt types}, 584
-  \item {\ptt tyvars}, 588
-  \item {\ptt tyvarsl}, 589
-
-  \indexspace
-
-  \item {\ptt uncurry}, 590
-  \item {\ptt UNCURRY\_DEF}, 617
-  \item {\ptt UNDISCH}, 590
-  \item {\ptt UNDISCH\_ALL}, 591
-  \item {\ptt UNDISCH\_TAC}, 592
-  \item {\ptt undo\_autoload}, 592
-  \item {\ptt unhide\_constant}, 593
-  \item {\ptt union}, 593
-  \item {\ptt unlink}, 594
-  \item {\ptt UNZIP}, 658
-  \item {\ptt UNZIP\_FST\_DEF}, 658
-  \item {\ptt UNZIP\_SND\_DEF}, 658
-  \item {\ptt UNZIP\_SNOC}, 658
-  \item {\ptt UNZIP\_ZIP}, 658
-
-  \indexspace
-
-  \item {\ptt VALID}, 594
-  \item {\ptt variant}, 595
-  \item {\ptt vars}, 596
-  \item {\ptt varsl}, 597
-  \item {\ptt version}, 598
-
-  \indexspace
-
-  \item {\ptt W}, 598
-  \item {\ptt WOP}, 633
-  \item {\ptt word\_separators}, 600
-  \item {\ptt words}, 598
-  \item {\ptt words2}, 599
-  \item {\ptt write}, 600
-
-  \indexspace
-
-  \item {\ptt X\_CASES\_THEN}, 601
-  \item {\ptt X\_CASES\_THENL}, 603
-  \item {\ptt X\_CHOOSE\_TAC}, 604
-  \item {\ptt X\_CHOOSE\_THEN}, 605
-  \item {\ptt X\_FUN\_EQ\_CONV}, 607
-  \item {\ptt X\_GEN\_TAC}, 607
-  \item {\ptt X\_SKOLEM\_CONV}, 608
-
-  \indexspace
-
-  \item {\ptt ZERO\_DEF}, 633
-  \item {\ptt ZERO\_DIV}, 633
-  \item {\ptt ZERO\_LESS\_EQ}, 633
-  \item {\ptt ZERO\_LESS\_EXP}, 633
-  \item {\ptt ZERO\_MOD}, 633
-  \item {\ptt ZERO\_REP\_DEF}, 633
-  \item {\ptt ZIP}, 659
-  \item {\ptt ZIP\_SNOC}, 659
-  \item {\ptt ZIP\_UNZIP}, 659
-
+egin{theindex}
+\mbox{}
 \end{theindex}
--- hol88-2.02.19940316.orig/Manual/Tutorial/tutorial.tex
+++ hol88-2.02.19940316/Manual/Tutorial/tutorial.tex
@@ -38,7 +38,7 @@
 
    \include{title}			  % tutorial title page
    \include{preface}		          % preface to entire tutorial
-   \include{../LaTeX/ack}		  % global acknowledgements
+   \include{ack}		          % global acknowledgements
    \include{contents}		          % table of contents   
 
    \pagenumbering{arabic}		 % arabic page numbers
--- hol88-2.02.19940316.orig/Manual/Description/description.tex
+++ hol88-2.02.19940316/Manual/Description/description.tex
@@ -34,7 +34,7 @@
 
    \include{title}			  % description title page
    \include{preface}		          % preface to entire description
-   \include{../LaTeX/ack}	          % global acknowledgements
+   \include{ack}	                  % global acknowledgements
    \include{contents}		          % table of contents   
 
 
--- hol88-2.02.19940316.orig/Manual/LaTeX/ref-macros.tex
+++ hol88-2.02.19940316/Manual/LaTeX/ref-macros.tex
@@ -172,3 +172,8 @@
 % ---------------------------------------------------------------------
 
 \def\none{{\it none}}
+
+\newcommand\nintt{\fontsize{9pt}{11pt}\normalfont\ttfamily}
+\newcommand\tenrm{\fontsize{10pt}{12pt}\normalfont\rmfamily}
+%\def\ptt{\fam\ttfam\nintt}\textfont\ttfam\nintt\scriptfont\ttfam\nintt\scriptscriptfont\ttfam\nintt
+\def\ptt{\fam\ttfam\nintt}%\textfont\ttfam\nintt\scriptfont\ttfam\nintt\scriptscriptfont\ttfam\nintt
--- hol88-2.02.19940316.orig/Manual/LaTeX/layout.sty
+++ hol88-2.02.19940316/Manual/LaTeX/layout.sty
@@ -52,9 +52,9 @@
 % MATH INDENTATION.  = \tabcolsep + three small verbatim spaces  (!)
 % ---------------------------------------------------------------------
 \setlength{\mathindent}{\tabcolsep}
-\addtolength{\mathindent}{\the\fontdimen2\elvtt}
-\addtolength{\mathindent}{\the\fontdimen2\elvtt}
-\addtolength{\mathindent}{\the\fontdimen2\elvtt}
+%\addtolength{\mathindent}{\the\fontdimen2\elvtt}
+%\addtolength{\mathindent}{\the\fontdimen2\elvtt}
+%\addtolength{\mathindent}{\the\fontdimen2\elvtt}
 
 % ---------------------------------------------------------------------
 % HEAD: spacing to match header macro below.
--- hol88-2.02.19940316.orig/Manual/Covers/Makefile
+++ hol88-2.02.19940316/Manual/Covers/Makefile
@@ -20,12 +20,12 @@
 
 endpages.dvi: CRC.ps DESCRIPTION.ps LANTERN.ps REFERENCE.ps TUTORIAL.ps \
               arms.ps endpages.tex endpages.sty
-	$(LATEX) endpages
+	TEXINPUTS=$$(pwd)/psfig:$$TEXINPUTS $(LATEX) endpages
 	@echo "===> endpages.dvi created"
 
 titlepages.dvi: CRC.ps DESCRIPTION.ps LANTERN.ps REFERENCE.ps TUTORIAL.ps \
                 arms.ps titlepages.tex titlepages.sty
-	$(LATEX) titlepages
+	TEXINPUTS=$$(pwd)/psfig:$$TEXINPUTS $(LATEX) titlepages
 	@echo "===> titlepages.dvi created"
 
 dvi: endpages.dvi titlepages.dvi