Definition idtoiso_2_1_alt_E₂ {x y : E₂} (f g : x --> y) (HC_2_1 : is_univalent_2_1 C) (HD₁_2_1 : disp_univalent_2_1 D₁) (HD₂_2_1 : disp_univalent_2_1 D₂) : f = g ≃ invertible_2cell f g. Proof. refine ((iso_in_E₂_weq f g) ∘ (idtoiso_2_1 _ _ ,, _) ∘ path_mor_E₂_to_path_mor_E₁_weq f g)%weq. apply E₁_univalent_2_1; assumption. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.