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