proposition: Theorem Identity_IsApplicative : IsApplicative Identity_IsFunctor Identity_Applicative.
proof: Proof. construct. - apply Id_LaxMonoidalFunctor. - 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