Lemma montrafotargetbicat_tensor_comp_aux_inst2 (v v' w : V) (f : V ⟦ v, v' ⟧) (η : G · FA' v ==> FA v · G) (η' : G · FA' v' ==> FA v' · G) (π : G · FA' w ==> FA w · G): η • (# FA f ▹ G) = (G ◃ # FA' f) • η' → param_distr_bicat_pentagon_eq_body_variant_RHS v w η π • (# FA (f ⊗^{ Mon_V}_{r} w) ▹ G) = (G ◃ # FA' (f ⊗^{ Mon_V}_{r} w)) • param_distr_bicat_pentagon_eq_body_variant_RHS v' w η' π. Proof. intro Hyp. rewrite <- (when_bifunctor_becomes_rightwhiskering Mon_V). change (montrafotargetbicat_disp w) in π. exact (montrafotargetbicat_tensor_comp_aux v w v' w f (identity w) η π η' π Hyp (id_disp π)). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.MonoidalSections. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrength. Require Import UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Import Bicat.Notations. Import BifunctorNotations. Import DisplayedBifunctorNotations. Import MonoidalNotations. Section FromMonoidalSectionBicat. End FromMonoidalSectionBicat. Section FromMonoidalSection. End FromMonoidalSection.