src/LCF/ex/Ex3.thy
author haftmann
Mon, 05 Jul 2010 15:12:20 +0200
changeset 37715 44b27ea94a16
parent 35762 af3ff2ba4c54
child 47025 b2b8ae61d6ad
permissions -rw-r--r--
tuned proof

header {* Addition with fixpoint of successor *}

theory Ex3
imports LCF
begin

consts
  s     :: "'a => 'a"
  p     :: "'a => 'a => 'a"

axioms
  p_strict:     "p(UU) = UU"
  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 (no_asm))
  apply (simp (no_asm))
  done

end