Definition from_is_disp_invertible_2cell_over_id_lift (Hττ : is_disp_invertible_2cell (id2_invertible_2cell _) ττ) : is_disp_invertible_2cell (D := D₂) (id2_invertible_2cell _) ττ. Proof. refine (pr1 Hττ ,, _ ,, _). - abstract (refine (pr12 Hττ @ _) ; rewrite lift_transportb ; apply maponpaths_2 ; apply cellset_property). - abstract (refine (pr22 Hττ @ _) ; rewrite lift_transportb ; apply maponpaths_2 ; apply cellset_property). 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.