--- a/doc-src/Logics/FOL.tex Fri Apr 22 18:18:37 1994 +0200
+++ b/doc-src/Logics/FOL.tex Fri Apr 22 18:43:49 1994 +0200
@@ -35,9 +35,9 @@
Some intuitionistic derived rules are shown in
Fig.\ts\ref{fol-int-derived}, again with their \ML\ names. These include
rules for the defined symbols $\neg$, $\bimp$ and $\exists!$. Natural
-deduction typically involves a combination of forwards and backwards
+deduction typically involves a combination of forward and backward
reasoning, particularly with the destruction rules $(\conj E)$,
-$({\imp}E)$, and~$(\forall E)$. Isabelle's backwards style handles these
+$({\imp}E)$, and~$(\forall E)$. Isabelle's backward style handles these
rules badly, so sequent-style rules are derived to eliminate conjunctions,
implications, and universal quantifiers. Used with elim-resolution,
\tdx{allE} eliminates a universal quantifier while \tdx{all_dupE}
@@ -45,7 +45,7 @@
conj_impE}, etc., support the intuitionistic proof procedure
(see~\S\ref{fol-int-prover}).
-See the files {\tt FOL/ifol.thy}, {\tt FOL/ifol.ML} and
+See the files {\tt FOL/IFOL.thy}, {\tt FOL/IFOL.ML} and
{\tt FOL/intprover.ML} for complete listings of the rules and
derived rules.
@@ -360,7 +360,7 @@
generally unsuitable for depth-first search.
\end{ttdescription}
\noindent
-See the file {\tt FOL/fol.ML} for derivations of the
+See the file {\tt FOL/FOL.ML} for derivations of the
classical rules, and
\iflabelundefined{chap:classical}{the {\em Reference Manual\/}}%
{Chap.\ts\ref{chap:classical}}
@@ -582,7 +582,7 @@
{\out 1. !!x. [| ALL y. ~ (ALL x. P(y) --> P(x)); P(?a) |] ==> P(x)}
\end{ttbox}
By the duality between $\exists$ and~$\forall$, applying~$(\forall E)$
-effectively applies~$(\exists I)$ again.
+in effect applies~$(\exists I)$ again.
\begin{ttbox}
by (eresolve_tac [allE] 1);
{\out Level 4}
@@ -622,7 +622,7 @@
{\out EX y. ALL x. P(y) --> P(x)}
{\out No subgoals!}
\end{ttbox}
-The civilized way to prove this theorem is through \ttindex{best_tac},
+The civilised way to prove this theorem is through \ttindex{best_tac},
supplying the classical version of~$(\exists I)$:
\begin{ttbox}
goal FOL.thy "EX y. ALL x. P(y)-->P(x)";
@@ -778,8 +778,8 @@
{\out 3. [| ~ P; if(Q,C,D) |] ==> if(Q,if(P,A,C),if(P,B,D))}
{\out 4. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D))}
\end{ttbox}
-
-In the first two subgoals, all formulae have been reduced to atoms. Now
+%
+In the first two subgoals, all assumptions have been reduced to atoms. Now
$if$-introduction can be applied. Observe how the $if$-rules break down
occurrences of $if$ when they become the outermost connective.
\begin{ttbox}