proposition: Lemma update_cons_match : forall n v x l, update n v (x::l) = match n with | 0 => v::l | S n' => x::(update n' v l) end.
proof: Proof. Proof using. auto. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)