doc-src/TutorialI/Misc/Plus.thy
author wenzelm
Fri, 27 Jan 2006 19:03:07 +0100
changeset 18801 b913ce69660c
parent 16417 9bc16273c2d4
child 19249 86c73395c99b
permissions -rw-r--r--
moved theorem tags from Drule to PureThy; replaced kind attribute by kind string; tuned name_multi: index > 1 only; added note_thmss_qualified (from Isar/locale.ML);

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

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

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

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

end
(*>*)