(** 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 valid_val_ge_id: forall fg f b i (Hvalid: valid_val fg (Vptr b i)) (Hincr: ren_incr fg f) (Hfg: forall b1 b2, fg b1 = Some b2 -> b1 = b2), f b = Some b.