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

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

Lemma notin_dests_append: forall d m1 m2, ~In d (dests (m1 ++ m2)) <-> ~In d (dests m1) /\ ~In d (dests m2).