proposition: Lemma nth_gt_length : forall l n, n >= length l -> nth n l = arbitrary.
proof: Proof. Proof using. introv N. applys~ nth_default_gt_length. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)