(** [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 env_equiv_trans: forall e1 e2 e3, env_equiv e1 e2 -> env_equiv e2 e3 -> env_equiv e1 e3.