Introduced the function some_elem for grabbing an element from a non-empty set, and simplified the theorem the_elem_image_unique
(*<*)
theory fakenat imports Main begin
(*>*)
text\<open>\noindent
The type \tydx{nat} of natural
numbers is predefined to have the constructors \cdx{0} and~\cdx{Suc}.
It behaves approximately as if it were declared like this:
\<close>
datatype nat = zero ("0") | Suc nat
(*<*)
end
(*>*)