proposition: Lemma notin_flat_map_Forall A B : forall (f : A -> list B) x l, ~ In x (flat_map f l) <-> Forall (fun y => ~ In x (f y)) l.
proof: Proof. intros f x l; rewrite Forall_Exists_neg. apply not_iff_compat, in_flat_map_Exists. Qed.
imports: PeanoNat