Definition trivial_is_univalent_2_1 {B C : bicat} (HC : is_univalent_2_1 C) : disp_univalent_2_1 (trivial_displayed_bicat B C). Proof. use fiberwise_local_univalent_is_univalent_2_1. intros b₁ b₂ f c₁ c₂ ff gg. use weqhomot. - exact (trivial_invertible_2cell_weq_disp_invertible ff gg ∘ make_weq (idtoiso_2_1 ff gg) (HC _ _ ff gg))%weq. - intro p ; cbn in p. induction p. use subtypePath. { intro ; apply isaprop_is_disp_invertible_2cell. } 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.