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

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

Lemma dests_disjoint_cons_right: forall m1 s d m2, dests_disjoint m1 ((s, d) :: m2) <-> dests_disjoint m1 m2 /\ ~In d (dests m1).