proposition: Lemma Nth_nth : forall l n, n < length l -> Nth n l (nth n l).
proof: Proof. Proof using. intros. applys* Nth_of_nth. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)