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_undef_nondata_regs: forall ms sp rl rs, agree ms sp rs -> (forall r, In r rl -> data_preg r = false) -> agree ms sp (undef_regs rl rs).