proposition: Lemma Nth_inv_neq_nil : forall n l x, Nth n l x -> l <> nil.
proof: Proof. Proof using. introv H. inverts H; auto_false. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)