proposition: Lemma update_succ : forall n v x l, update (S n) v (x::l) = x::(update n v l).
proof: Proof. Proof using. auto. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)