Arguments measure_ind {X}.

(* induction principle wrt. a decreasing measure f *)
(* example: elim /(measure_ind length) : l. *)
Lemma measure_rect {X : Type} (f : X -> nat) (P : X -> Type) :
(forall x, (forall y, f y < f x -> P y) -> P x) -> forall (x : X), P x.