Proof with auto.
induction l...
simpl.
intros.
rewrite IHl...
rewrite H...
Qed.

(* Specifications: *)
Lemma repeat_plus T (c: T) n m: repeat (n + m) c = repeat n c ++ repeat m c.
Lemma filter_perms T p (l: list T):
Permutation
(map (filter p) (perms l))
(concat (map (repeat (fact (length (filter (negb ∘ p) l)) * length (merges (filter p l) (filter (negb ∘ p) l)))) (perms (filter p l)))).