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

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

Lemma notin_dests_cons: forall x s d m, ~In x (dests ((s, d) :: m)) <-> x <> d /\ ~In x (dests m).