proposition: Theorem arrow_IsMonad {x} : IsMonad arrow_IsFunctor arrow_IsApplicative (arrow_Monad x).
proof: Proof. unfold arrow_Monad, arrow. construct; auto. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Monad Category.Theory.Functor Category.Functor.Applicative Category.Monad.Distributive Category.Monad.Compose Category.Functor.Structure.Monoidal.Pure Category.Instance.Coq Category.Theory.Coq.Applicative.Proofs Category.Theory.Coq.Monad