Lemma z_iso_disp_aux_weq (U1 : is_univalent_in_fibers D1) (U2 : is_univalent_in_fibers D2) (x : C) (xx xx' : D1 x × D2 x) : xx = xx' ≃ @z_iso_disp _ dirprod_disp_cat _ _ (identity_z_iso x) xx xx'. Proof. eapply weqcomp. apply pathsdirprodweq. apply invweq. eapply weqcomp. apply z_iso_disp_prod_weq. apply invweq. apply weqdirprodf. - exists idtoiso_fiber_disp. apply U1. - exists idtoiso_fiber_disp. apply U2. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.