proposition: Lemma length_last : forall x l, length (l & x) = 1 + length l.
proof: Proof. Proof using. intros. rewrite length_app, length_cons, length_nil. simpl. math. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)