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