Definition sigma_is_univalent_2_0 (HC : is_univalent_2 C) (HD₁ : disp_univalent_2 D₁) (HD₂ : disp_univalent_2 D₂) : is_univalent_2_0 E₂. Proof. intros x y. use weqhomot. - exact (idtoiso_2_0_alt_E₂ x y HC HD₁ HD₂). - intros p. induction p. use subtypePath. { intro. apply isaprop_left_adjoint_equivalence. apply sigma_is_univalent_2_1. - exact (pr2 HC). - exact (pr2 HD₁). - exact (pr2 HD₂). } reflexivity. 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.