(** [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 state_wf_start: forall mu, move_no_temp mu -> is_mill mu -> state_wf (State mu nil nil).