Lemma montrafotargetbicat_pentagon_eq: pentagon_eq montrafotargetbicat_tensor montrafotargetbicat_associator. Proof. intros vη1 vη2 vη3 vη4. use total2_paths_f. + cbn. repeat rewrite id_left. repeat rewrite id_right. assert (pentagoninst := monoidal_cat_pentagon_eq Mon_V (pr1 vη1) (pr1 vη2) (pr1 vη3) (pr1 vη4)). exact pentagoninst. + apply trafotargetbicat_disp_cells_isaprop. 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.DisplayedMonoidalTensored. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrength. Require Import UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory. 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.