--- a/doc-src/TutorialI/Recdef/document/Nested1.tex Fri Jan 12 16:05:12 2001 +0100
+++ b/doc-src/TutorialI/Recdef/document/Nested1.tex Fri Jan 12 16:07:20 2001 +0100
@@ -5,7 +5,7 @@
\begin{isamarkuptext}%
\noindent
Although the definition of \isa{trev} is quite natural, we will have
-overcome a minor difficulty in convincing Isabelle of is termination.
+to overcome a minor difficulty in convincing Isabelle of its termination.
It is precisely this difficulty that is the \textit{raison d'\^etre} of
this subsection.
@@ -27,12 +27,13 @@
where \isa{set} returns the set of elements of a list
and \isa{term{\isacharunderscore}list{\isacharunderscore}size\ {\isacharcolon}{\isacharcolon}\ term\ list\ {\isasymRightarrow}\ nat} is an auxiliary
function automatically defined by Isabelle
-(when \isa{term} was defined). First we have to understand why the
+(while processing the declaration of \isa{term}). First we have to understand why the
recursive call of \isa{trev} underneath \isa{map} leads to the above
condition. The reason is that \isacommand{recdef} ``knows'' that \isa{map}
-will apply \isa{trev} only to elements of \isa{ts}. Thus the above
+will apply \isa{trev} only to elements of \isa{ts}. Thus the
condition expresses that the size of the argument \isa{t\ {\isasymin}\ set\ ts} of any
-recursive call of \isa{trev} is strictly less than \isa{size\ {\isacharparenleft}App\ f\ ts{\isacharparenright}\ {\isacharequal}\ Suc\ {\isacharparenleft}term{\isacharunderscore}list{\isacharunderscore}size\ ts{\isacharparenright}}. We will now prove the termination condition and
+recursive call of \isa{trev} is strictly less than \isa{size\ {\isacharparenleft}App\ f\ ts{\isacharparenright}},
+which equals \isa{Suc\ {\isacharparenleft}term{\isacharunderscore}list{\isacharunderscore}size\ ts{\isacharparenright}}. We will now prove the termination condition and
continue with our definition. Below we return to the question of how
\isacommand{recdef} ``knows'' about \isa{map}.%
\end{isamarkuptext}%