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

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

Lemma path_sources_dests: forall s0 d0 sigma, is_path (sigma ++ (s0, d0) :: nil) -> List.incl (srcs (sigma ++ (s0, d0) :: nil)) (s0 :: dests (sigma ++ (s0, d0) :: nil)).