src/LCF/ex/Ex3.thy
author wenzelm
Sat, 05 Apr 2014 15:03:40 +0200
changeset 56421 1ffd7eaa778b
parent 47025 b2b8ae61d6ad
child 58889 5b7a9633cfa8
permissions -rw-r--r--
updated to jedit_build-20140405: Code2HTML.jar, CommonControls.jar, Console.jar, kappalayout.jar, Navigator.jar, SideKick.jar, doc with jEdit manuals (ant dist-manuals);

header {* Addition with fixpoint of successor *}

theory Ex3
imports LCF
begin

axiomatization
  s     :: "'a => 'a" and
  p     :: "'a => 'a => 'a"
where
  p_strict:     "p(UU) = UU" and
  p_s:          "p(s(x),y) = s(p(x,y))"

declare p_strict [simp] p_s [simp]

lemma example: "p(FIX(s),y) = FIX(s)"
  apply (tactic {* induct_tac @{context} "s" 1 *})
  apply simp
  apply simp
  done

end