Definition disp_map_bicat_to_disp_cat_id_comp : disp_cat_id_comp B disp_map_bicat_to_disp_cat_ob_mor. Proof. split. - intros y h. use make_disp_map_bicat_mor. + exact (id₁ _). + apply id_pred_mor. + exact (comp_of_invertible_2cell (runitor_invertible_2cell _) (linvunitor_invertible_2cell _)). - intros y₁ y₂ y₃ g₁ g₂ h₁ h₂ h₃ f₁ f₂. use make_disp_map_bicat_mor. + exact (pr1 f₁ · pr1 f₂). + exact (comp_pred_mor D (pr12 f₁) (pr12 f₂)). + exact (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ (pr22 f₁)) (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ (pr22 f₂)) (lassociator_invertible_2cell _ _ _))))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.Limits.Pullbacks.