(** [env_equiv] is an equivalence relation between environments
  capturing the fact that two environments assign the same values to
  non-temporary registers, but can disagree on the values of temporary
  registers. *)

Definition env_equiv (e1 e2: env) : Prop :=
  forall r, is_not_temp r -> e1 r = e2 r.

Lemma exec_par_env_equiv: forall m e1 e2, move_no_temp m -> env_equiv e1 e2 -> env_equiv (exec_par m e1) (exec_par m e2).