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

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).