(** 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.