Using type real does not require a separate logic now.
(*<*)
theory fakenat imports Main begin;
(*>*)
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
(*>*)