src/Doc/Tutorial/Misc/Plus.thy
author wenzelm
Fri, 07 Nov 2014 16:13:05 +0100
changeset 58926 baf5a3c28f0c
parent 48985 5386df44a037
child 67406 23307fd33906
permissions -rw-r--r--
proper import of Main: BNF_Least_Fixpoint does not "contain pretty much everything", especially it lacks the 'value' command, which is defined *after* theory List;

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

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

primrec add :: "nat \<Rightarrow> nat \<Rightarrow> nat" where
"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
(*>*)