Definition disp_invertible_2cell_weq_lift {x y : E} {f g : x --> y} (τ : invertible_2cell f g) {xx : lift_disp_bicat x} {yy : lift_disp_bicat y} (ff : xx -->[ f ] yy) (gg : xx -->[ g ] yy) : disp_invertible_2cell (D := D₂) (make_invertible_2cell (pr1_invertible_2cell_total _ τ)) ff gg ≃ disp_invertible_2cell τ ff gg. Proof. use weqfibtototal. intro ττ. apply is_disp_invertible_2cell_weq_lift. 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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Section FromLift. End FromLift.