Definition make_disp_univ_arrow_if_groupoid_and_prop : disp_left_universal_arrow LUR RR. Proof. use make_disp_univ_arrow_if_prop. - exact D1_2cells_prop. - exact D2_2cells_prop. - exact LL. - exact ηη. - exact LL_mor. - exact LL_2cell. - exact LL_unit. - intros x xx y yy f ff. use (pr1 (disp_hom_disp_invertible_2cell_to_z_iso _ _)). + apply LL_unit. + apply (D1_2cells_grp _ _ _ _ (_ ,, (pr12 (adj x y)) f)). - exact LL_counit. - intros x xx y yy f ff. use (pr1 (disp_hom_disp_invertible_2cell_to_z_iso _ _)). + apply LL_counit. + apply (D2_2cells_grp _ _ _ _ (_ ,, (pr22 (adj x y)) f)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Adjunctions. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.TotalAdjunction. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.PseudoFunctors.UniversalArrow. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBiadjunction. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Import DispBicat.Notations.