--- a/doc-src/TutorialI/Misc/document/natsum.tex Thu Nov 29 20:02:23 2001 +0100
+++ b/doc-src/TutorialI/Misc/document/natsum.tex Thu Nov 29 21:12:37 2001 +0100
@@ -34,7 +34,7 @@
\newcommand{\mystar}{*%
}
\index{arithmetic operations!for \protect\isa{nat}}%
-The usual arithmetic operations \ttindexboldpos{+}{$HOL2arithfun},
+The arithmetic operations \ttindexboldpos{+}{$HOL2arithfun},
\ttindexboldpos{-}{$HOL2arithfun}, \ttindexboldpos{\mystar}{$HOL2arithfun},
\sdx{div}, \sdx{mod}, \cdx{min} and
\cdx{max} are predefined, as are the relations
@@ -47,8 +47,8 @@
\ttindexboldpos{+}{$HOL2arithfun}, \ttindexboldpos{-}{$HOL2arithfun},
\ttindexboldpos{\mystar}{$HOL2arithfun}, \cdx{min},
\cdx{max}, \indexboldpos{\isasymle}{$HOL2arithrel} and
- \ttindexboldpos{<}{$HOL2arithrel} are overloaded, i.e.\ they are available
- not just for natural numbers but at other types as well.
+ \ttindexboldpos{<}{$HOL2arithrel} are overloaded: they are available
+ not just for natural numbers but for other types as well.
For example, given the goal \isa{x\ {\isacharplus}\ {\isadigit{0}}\ {\isacharequal}\ x}, there is nothing to indicate
that you are talking about natural numbers. Hence Isabelle can only infer
that \isa{x} is of some arbitrary type where \isa{{\isadigit{0}}} and \isa{{\isacharplus}} are
@@ -65,7 +65,7 @@
overloaded operations.
\end{warn}
\begin{warn}
- Constant \isa{{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat} is defined to be \isa{Suc\ {\isadigit{0}}}. This definition
+ Constant \isa{{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat} is defined to equal \isa{Suc\ {\isadigit{0}}}. This definition
(see \S\ref{sec:ConstDefinitions}) is unfolded automatically by some
tactics (like \isa{auto}, \isa{simp} and \isa{arith}) but not by
others (especially the single step tactics in Chapter~\ref{chap:rules}).