(** [list_disjoint l1 l2] holds iff [l1] and [l2] have no elements in common. *)
Definition list_disjoint (A: Type) (l1 l2: list A) : Prop :=
forall (x y: A), In x l1 -> In y l2 -> x <> y.

Lemma list_disjoint_sym:
forall (A: Type) (l1 l2: list A),
list_disjoint l1 l2 -> list_disjoint l2 l1.