doc-src/TutorialI/Misc/fakenat.thy

proof by cases and induction on types and sets (used to be specific for HOL);

(*<*)
theory fakenat = Main:;
(*>*)

text{*\noindent
The type \tydx{nat} of natural
numbers is predefined to have the constructors \cdx{0} and~\cdx{Suc}.  It  behaves as if it were declared like this:
*}

datatype nat = 0 | Suc nat
(*<*)
end
(*>*)