Definition sigma_prebicat_1_id_comp_cells : disp_prebicat_1_id_comp_cells C. Proof. exists sigma_disp_cat_data. red. intros c c' f g x d d' ff gg. cbn in *. use (∑ xx : pr1 ff ==>[x] pr1 gg , _). set (PPP := @prebicat_cells (total_bicat D) (c,, pr1 d) (c',, pr1 d') (f,, pr1 ff) (g,, pr1 gg)). exact (pr2 ff ==>[(x,, xx) : PPP] pr2 gg). Defined.
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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.