(** Some properties of [is_mill] and [dests_disjoint]. *)

Definition dests_disjoint (m1 m2: moves) : Prop :=
  list_disjoint (dests m1) (dests m2).

Lemma temp_last_push: forall s1 d1 s2 d2 sigma, temp_last ((s2, d2) :: sigma) -> is_not_temp s1 -> is_not_temp d1 -> temp_last ((s1, d1) :: (s2, d2) :: sigma).