Fixpoint preg_notin (r: preg) (rl: list mreg) : Prop :=
  match rl with
  | nil => True
  | r1 :: nil => r <> preg_of r1
  | r1 :: rl => r <> preg_of r1 /\ preg_notin r rl
  end.Remark preg_notin_charact:
  forall r rl,
  preg_notin r rl <-> (forall mr, In mr rl -> r <> preg_of mr).

(* Specifications: *)
Lemma undef_regs_other_2: forall r rl rs, preg_notin r rl -> undef_regs (map preg_of rl) rs r = rs r.
Lemma preg_vals: forall ms sp rs, agree ms sp rs -> forall l, Val.lessdef_list (map ms l) (map rs (map preg_of l)).