(** Results about id injections*)
Definition id_ren m :=
fun b => if is_left (valid_block_dec m b) then Some b else None.
Hint Unfold id_ren.

Lemma incr_domain_id:
forall m f f'
(Hincr: ren_incr f f')
(Hf_id: forall b b', f b = Some b' -> b = b')
(Hdomain_f: domain_memren f' m),
ren_incr f (id_ren m).