proposition: Lemma list_same_length_inv_nil : forall l1 l2, length l1 = length l2 -> l1 = nil <-> l2 = nil.
proof: Proof. Proof using. intros. destruct l1; destruct l2; auto_false*. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)