Definition from_is_disp_invertible_2cell_lift (Hττ : is_disp_invertible_2cell Hτ ττ) : is_disp_invertible_2cell (D := D₂) (pr1_invertible_2cell_total _ Hτ) ττ. Proof. refine (pr1 Hττ ,, _ ,, _). - abstract (refine (pr12 Hττ @ _) ; rewrite lift_transportb ; apply idpath). - abstract (refine (pr22 Hττ @ _) ; rewrite lift_transportb ; apply idpath). 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.