(** 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_trans: forall f f' f'' rs rs' rs'', regset_ren f rs rs'' -> regset_ren f' rs rs' -> (forall b b' b'' : block, f b = Some b'' -> f' b = Some b' -> f'' b' = Some b'') -> regset_ren f'' rs' rs''.