Definition trivial_is_univalent_2_0 {B C : bicat} (HB_2_1 : is_univalent_2_1 B) (HC_2_0 : is_univalent_2_0 C) (HC_2_1 : is_univalent_2_1 C) : disp_univalent_2_0 (trivial_displayed_bicat B C). Proof. use fiberwise_univalent_2_0_to_disp_univalent_2_0. intros b c₁ c₂. use weqhomot. - exact (trivial_adj_equiv_weq_disp_adj_equiv HB_2_1 HC_2_1 c₁ c₂ ∘ make_weq (idtoiso_2_0 c₁ c₂) (HC_2_0 c₁ c₂))%weq. - intros p. cbn in p. induction p. use subtypePath. { intro. use isaprop_disp_left_adjoint_equivalence. - exact HB_2_1. - apply trivial_is_univalent_2_1. exact HC_2_1. } 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.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.