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