Definition disp_hom_id_comp {x y : B} (xx : D x) (yy : D y) : disp_cat_id_comp _ (disp_hom_ob_mor xx yy). Proof. simple refine (_ ,, _). - exact (λ f ff, disp_id2 ff). - exact (λ f g h α β ff gg hh αα ββ, αα •• ββ). 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.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.