Definition montrafotargetbicat_right_unitor: right_unitor montrafotargetbicat_tensor montrafotargetbicat_unit. Proof. use make_nat_z_iso. + use make_nat_trans. * intro vη. exists (monoidal_cat_right_unitor Mon_V (pr1 vη)). apply montrafotargetbicat_right_unitor_aux1. * intros vη vη' fg. use total2_paths_f. -- cbn. do 3 rewrite id_left. rewrite id_right. apply (nat_trans_ax (monoidal_cat_right_unitor Mon_V)). -- apply trafotargetbicat_disp_cells_isaprop. + intro vη. use make_is_z_isomorphism. * exists (pr1 (pr2 (monoidal_cat_right_unitor Mon_V) (pr1 vη))). apply montrafotargetbicat_right_unitor_aux2. * split. -- use total2_paths_f. ++ cbn. apply (pr2 (pr2 (monoidal_cat_right_unitor Mon_V) (pr1 vη))). ++ apply trafotargetbicat_disp_cells_isaprop. -- use total2_paths_f. ++ cbn. apply (pr2 (pr2 (monoidal_cat_right_unitor Mon_V) (pr1 vη))). ++ apply trafotargetbicat_disp_cells_isaprop. Defined.
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.