--- a/doc-src/Logics/CTT.tex Fri Apr 22 18:18:37 1994 +0200
+++ b/doc-src/Logics/CTT.tex Fri Apr 22 18:43:49 1994 +0200
@@ -395,8 +395,8 @@
Elimination rules have the suffix~{\tt E}\@. Computation rules, which
describe the reduction of eliminators, have the suffix~{\tt C}\@. The
equality versions of the rules (which permit reductions on subterms) are
-called {\em long} rules; their names have the suffix~{\tt L}\@.
-Introduction and computation rules often are further suffixed with
+called {\bf long} rules; their names have the suffix~{\tt L}\@.
+Introduction and computation rules are often further suffixed with
constructor names.
Figure~\ref{ctt-equality} presents the equality rules. Most of them are
@@ -514,12 +514,12 @@
\end{ttbox}
Blind application of {\CTT} rules seldom leads to a proof. The elimination
rules, especially, create subgoals containing new unknowns. These subgoals
-unify with anything, causing an undirectional search. The standard tactic
+unify with anything, creating a huge search space. The standard tactic
\ttindex{filt_resolve_tac}
(see \iflabelundefined{filt_resolve_tac}{the {\em Reference Manual\/}}%
{\S\ref{filt_resolve_tac}})
%
-can reject overly flexible goals; so does the {\CTT} tactic {\tt
+fails for goals that are too flexible; so does the {\CTT} tactic {\tt
test_assume_tac}. Used with the tactical \ttindex{REPEAT_FIRST} they
achieve a simple kind of subgoal reordering: the less flexible subgoals are
attempted first. Do some single step proofs, or study the examples below,
@@ -623,7 +623,7 @@
\item[\ttindexbold{safestep_tac} $thms$ $i$]
attacks subgoal~$i$ using formation rules and certain other `safe' rules
-(tdx{FE}, tdx{ProdI}, tdx{SumE}, tdx{PlusE}), calling
+(\tdx{FE}, \tdx{ProdI}, \tdx{SumE}, \tdx{PlusE}), calling
{\tt mp_tac} when appropriate. It also uses~$thms$,
which are typically premises of the rule being derived.
@@ -708,7 +708,6 @@
\[ a \bmod b + (a/b)\times b = a. \]
Figure~\ref{ctt-arith} presents the definitions and some of the key
theorems, including commutative, distributive, and associative laws.
-All proofs are on the file {\tt CTT/arith.ML}.
The operators~\verb'#+', \verb'-', \verb'|-|', \verb'#*', \verb'mod'
and~\verb'div' stand for sum, difference, absolute difference, product,
@@ -1065,7 +1064,7 @@
function $g\in \prod@{x\in A}C(x,f{\tt`}x)$.
In principle, the Axiom of Choice is simple to derive in Constructive Type
-Theory \cite[page~50]{martinlof84}. The following definitions work:
+Theory. The following definitions work:
\begin{eqnarray*}
f & \equiv & {\tt fst} \circ h \\
g & \equiv & {\tt snd} \circ h