Hint Extern 4 (_ el map _ _) => eapply in_map_iff.
Hint Extern 4 (_ el filter _ _) => eapply filter_In.
Fixpoint count (l : list nat) (n : nat)  :=
match l with
| [] => 0
| m :: l => if Nat.eqb n m then S (count l n) else count l n
end.

(* Specifications: *)
Lemma countSplit (A B: list nat) (x: nat)  : count A x + count B x = count (A ++ B) x.
Lemma notInZero (x: nat) A :
not (x el A) <-> count A x = 0.
Lemma countSplit (A B: list nat) (x: nat)  : count A x + count B x = count (A ++ B) x.
Lemma notInZero (x: nat) A :
not (x el A) <-> count A x = 0.