Definition is_univalent_in_fibers_from_univalent_disp {C} (D : disp_cat C) : is_univalent_disp D -> is_univalent_in_fibers D. Proof. unfold is_univalent_disp , is_univalent_in_fibers. intros H x xx xx'. specialize (H x x (idpath _ ) xx xx'). apply H. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.