Definition z_iso_weq_twosided_disp_cat_iso (x : C₁) (y : C₂) (z₁ z₂ : D) : z_iso z₁ z₂ ≃ @iso_twosided_disp _ _ constant_twosided_disp_cat _ _ _ _ (identity_z_iso x) (identity_z_iso y) z₁ z₂. Proof. use make_weq. - exact (z_iso_to_twosided_disp_cat_iso x y). - use isweq_iso. + exact (twosided_disp_cat_iso_to_z_iso x y). + abstract (intro f ; use subtypePath ; [ intro ; apply isaprop_is_z_isomorphism | ] ; cbn ; apply idpath). + abstract (intro f ; use subtypePath ; [ intro ; apply isaprop_is_iso_twosided_disp | ] ; cbn ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.