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

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

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