Theory Ex3

theory Ex3
imports LCF
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