(** 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_floats32_ren: forall f rs rs' v1 v2 v1' v2' (Hval_obs: val_obs f v1 v1') (Hval_obs': val_obs f v2 v2') (Hrs_ren: regset_ren f rs rs'), regset_ren f (compare_floats32 v1 v2 rs) (compare_floats32 v1' v2' rs').