proposition: Lemma nth_succ : forall n x l, nth (S n) (x::l) = nth n l.
proof: Proof. Proof using. intros. apply nth_default_succ. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)