(** 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 compare_ints_ren: forall f v1 v2 v1' v2' rs rs' m m' (Hval_obs: val_obs f v1 v1') (Hval_obs': val_obs f v2 v2') (Hrs_ren: regset_ren f rs rs') (Hmem_obs_eq: mem_obs_eq f m m'), regset_ren f (compare_ints v1 v2 rs m) (compare_ints v1' v2' rs' m').