(** Injections on registers *)

  Definition reg_ren f (r:PregEq.t) (rs rs' : regset) : Prop :=
    val_obs f (Pregmap.get r rs) (Pregmap.get r rs').Definition regset_ren f rs rs' : Prop :=
    forall r, reg_ren f r rs rs'.Definition core_inj f c c' :=
    match c, c' with State rs _, State rs' _ => regset_ren f rs rs' end.

Lemma mem_valid_alloc: forall m m' b lo hi f (Hdomain: domain_memren f m) (Hvalid_mem: valid_mem m) (Halloc: Mem.alloc m lo hi = (m', b)), valid_mem m' /\ (exists f', ren_domain_incr f f' /\ domain_memren f' m').