(** 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 regset_ren_init: forall f v v' (Hval_obs: val_obs f v v'), regset_ren f (Pregmap.init v) (Pregmap.init v').