Corollary agree_set_mreg_parallel:
  forall ms sp rs r v v',
  agree ms sp rs ->
  Val.lessdef v v' ->
  agree (Regmap.set r v ms) sp (Pregmap.set (preg_of r) v' rs).

Lemma agree_set_pair: forall sp p v v' ms rs, agree ms sp rs -> Val.lessdef v v' -> agree (Mach.set_pair p v ms) sp (set_pair (map_rpair preg_of p) v' rs).