Lemma isaprop_bidisp_unit_disp_2cell_struct {C D : bicat_of_univ_cats} {F G : bicat_of_univ_cats ⟦C,D⟧ } {α : prebicat_cells bicat_of_univ_cats F G} {IC : disp_unit_disp_cat_data C} {ID : disp_unit_disp_cat_data D} (puF : IC -->[ F] ID) (puG : IC -->[ G] ID) : isaprop (bidisp_unit_disp_2cell_struct C D F G α IC ID puF puG). Proof. apply isaprop_preservesunit_commutes. Qed.
Require Import UniMath.Foundations.All. 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.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories.