proposition: Theorem Compose_IsApplicative `(HF : EndoFunctor F) `(AF : @Functor.Applicative.Applicative _ _ (FromAFunctor HF)) `(HG : EndoFunctor G) `(AG : @Functor.Applicative.Applicative _ _ (FromAFunctor HG)) : IsApplicative (Compose_IsFunctor HF HG) (@Compose_Applicative F (EndoApplicative_Applicative HF AF) G (EndoApplicative_Applicative HG AG)).
proof: Proof. construct. - apply (@Compose_LaxMonoidalFunctor _ _ _ _ _ _ _ _ AF AG). - apply Coq_StrongFunctor. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Functor Category.Theory.Natural.Transformation Category.Structure.Monoidal.Closed Category.Functor.Structure.Monoidal Category.Functor.Structure.Monoidal.Pure Category.Functor.Structure.Monoidal.Id Category.Functor.Structure.Monoidal.Compose Category.Functor.Applicative Category.Instance.Coq Category.Theory.Coq.Functor.Proofs Category.Theory.Coq.Applicative