diff -r 4b47d8aaf5af -r 5eebea8f359f doc-src/TutorialI/Misc/natsum.thy --- a/doc-src/TutorialI/Misc/natsum.thy Thu Jan 25 11:59:52 2001 +0100 +++ b/doc-src/TutorialI/Misc/natsum.thy Thu Jan 25 15:31:31 2001 +0100 @@ -41,8 +41,8 @@ \ttindexboldpos{\mystar}{$HOL2arithfun}, \isaindexbold{min}, \isaindexbold{max}, \indexboldpos{\isasymle}{$HOL2arithrel} and \ttindexboldpos{<}{$HOL2arithrel} are overloaded, i.e.\ they are available - not just for natural numbers but at other types as well (see - \S\ref{sec:overloading}). For example, given the goal @{prop"x+0 = x"}, + not just for natural numbers but at other types as well. + For example, given the goal @{prop"x+0 = x"}, there is nothing to indicate that you are talking about natural numbers. Hence Isabelle can only infer that @{term x} is of some arbitrary type where @{term 0} and @{text"+"} are declared. As a consequence, you will be unable @@ -52,6 +52,10 @@ @{text"x+0 = (x::nat)"}. If there is enough contextual information this may not be necessary: @{prop"Suc x = x"} automatically implies @{text"x::nat"} because @{term Suc} is not overloaded. + + For details see \S\ref{sec:numbers} and \S\ref{sec:overloading}; + Table~\ref{tab:overloading} in the appendix shows the most important overloaded + operations. \end{warn} Simple arithmetic goals are proved automatically by both @{term auto} and the