Lemma step1 {x y : C} {xx : D x} {yy : D y} {f g : C⟦x,y⟧} {ff : xx -->[ f ] yy} {gg : xx -->[ g ] yy} : @invertible_2cell E (x ,, xx) (y ,, yy) (f,, ff) (g,, gg) ≃ (∑ (α : f ==> g) (αα : ff ==>[α] gg), ∑ (Hα : is_invertible_2cell α), is_disp_invertible_2cell Hα αα). Proof. eapply weqcomp. { apply weqfibtototal. intro. apply is_invertible_total_to_disp_weq. } eapply weqcomp. { apply weqinvweq. apply weqtotal2asstol. } apply idweq. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells.