Hint Constructors Permuted.

(* Specifications: *)
Lemma map_map_comp A B C (f: A -> B) (g: B -> C) (l: list A):
map g (map f l) = map (g ∘ f) l.
Lemma concat_map_singleton A (l: list A): concat (map (fun x => x :: nil) l) = l.
Lemma Permuted_sub A (R: relation A) x y: Permuted R x y -> forall (R': relation A), (forall x y, R x y -> R' x y) -> Permuted R' x y.
Proof with auto.