proposition: Lemma app_eq_nil_inv : forall l1 l2, l1 ++ l2 = nil -> l1 = nil /\ l2 = nil.
proof: Proof. Proof using. intros. destruct l1; destruct l2; intros; tryfalse~; auto. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)