(** 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 free_wd_domain : forall (m m' : mem) b lo hi (f : memren), domain_memren f m -> Mem.free m b lo hi = Some m' -> valid_mem m -> valid_mem m' /\ domain_memren f m'.