Definition idtoiso_2_0_alt_E₂ (x y : E₂) (HC : is_univalent_2 C) (HD₁ : disp_univalent_2 D₁) (HD₂ : disp_univalent_2 D₂) : x = y ≃ adjoint_equivalence x y. Proof. refine ((adjequiv_in_E₂_weq x y (pr2 HC) (pr2 HD₁) (pr2 HD₂)) ∘ (idtoiso_2_0 _ _ ,, _) ∘ path_E₂_to_path_E₁_weq x y)%weq. apply E₁_univalent_2_0. - exact (pr1 HC). - exact (pr1 HD₁). - exact (pr1 HD₂). 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.