doc-src/TutorialI/Misc/Plus.thy
author huffman
Sat, 20 Aug 2011 10:08:47 -0700
changeset 44346 00dd3c4dabe0
parent 27015 f8537d69f514
permissions -rw-r--r--
rename real_squared_diff_one_factored to square_diff_one_factored and move to Rings.thy

(*<*)
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
(*>*)