doc-src/TutorialI/Misc/Plus.thy

generalized types of of_nat and of_int to work with non-commutative types

(*<*)
theory Plus imports Main begin
(*>*)

text{*\noindent Define the following addition function *}

consts add :: "nat \<Rightarrow> nat \<Rightarrow> nat"
primrec
"add m 0 = m"
"add m (Suc n) = add (Suc m) n"

text{*\noindent and prove*}
(*<*)
lemma [simp]: "!m. add m n = m+n"
apply(induct_tac n)
by(auto)
(*>*)
lemma "add m n = m+n"
(*<*)
by(simp)

end
(*>*)