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

Lemma is_id_ren : forall f m (Hdomain: domain_memren f m) (Hf_id: forall b1 b2, f b1 = Some b2 -> b1 = b2), f = id_ren m.