proposition: Lemma Forall_app_inv : forall P l1 l2, Forall P (l1 ++ l2) -> Forall P l1 /\ Forall P l2.
proof: Proof. Proof using. introv H. rewrite* Forall_app_eq in H. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)