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

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

Lemma dests_disjoint_append_left: forall m1 m2 m3, dests_disjoint (m1 ++ m2) m3 <-> dests_disjoint m1 m3 /\ dests_disjoint m2 m3.