Lemma p1types_disp_univalent_2_0 : disp_univalent_2_0 p1types_disp. Proof. apply fiberwise_univalent_2_0_to_disp_univalent_2_0. intros X x x'. cbn in *. use isweq_iso. - intros f. apply f. - intro p. induction p. apply idpath. - intros [f Hf]. use subtypePath. { intros y y'. apply (isaprop_disp_left_adjoint_equivalence (D:=p1types_disp)). + apply one_types_is_univalent_2. + apply p1types_disp_univalent_2_1. } cbn ; cbn in f. induction f. apply idpath. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OneTypes. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.