Definition is_disp_invertible_2cell_weq_lift : is_disp_invertible_2cell (D := D₂) (pr1_invertible_2cell_total _ Hτ) ττ ≃ is_disp_invertible_2cell Hτ ττ. Proof. use weqimplimpl. - apply to_is_disp_invertible_2cell_lift. - apply from_is_disp_invertible_2cell_lift. - use (isaprop_is_disp_invertible_2cell (x := (_ ,, _))). - use (isaprop_is_disp_invertible_2cell (x := (_ ,, _))). 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.