proposition: Lemma measure_left_induction : forall (A : X -> Type) (z : t), (forall x, f x <= z -> (forall y, f x < f y <= z -> A y) -> A x) -> forall x, f x <= z -> A x.
proof: Proof. intros A z IH x Hx. enough (H : forall y, f y = f x -> A y) by now apply H. induction (gt_wf z (f x)) as [n _ IH']. intros y Hy. subst n. apply (IH y Hx). intros y' Hy'. now apply (IH' _ Hy'). Defined.
imports: NZAxioms NZBase Decidable OrdersTac