Lemma p1types_disp_univalent_2_1 : disp_univalent_2_1 p1types_disp. Proof. apply fiberwise_local_univalent_is_univalent_2_1. intros X Y f x y. cbn. intros p q. use isweq_iso. - intro α. apply α. - intros α. apply Y. - intros α. cbn in *. use subtypePath. { intro. apply (isaprop_is_disp_invertible_2cell (D:=p1types_disp)). } apply Y. 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.