proposition: Lemma nil_eq_app_inv : forall l1 l2, nil = l1 ++ l2 -> l1 = nil /\ l2 = nil.
proof: Proof. Proof using. intros. symmetry in H. apply* app_eq_nil_inv. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)