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

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

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