Remark return_measure_rec_incr:
  forall f n1 n2 pc,
  (n1 <= n2)%nat ->
  (return_measure_rec n1 f pc <= return_measure_rec n2 f pc)%nat.

(* Specifications: *)
Lemma is_return_measure_rec: forall f n n' pc r, is_return n f pc r = true -> (n <= n')%nat -> return_measure_rec n f.(fn_code) pc = return_measure_rec n' f.(fn_code) pc.
Lemma is_return_charact: forall f n pc rret, is_return n f pc rret = true -> (n <= niter)%nat -> is_return_spec f pc rret.