Definition iso_twosided_disp_weq_z_iso_disp {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} {x : C₁} {y : C₂} (xx yy : D x y) : iso_twosided_disp (identity_z_iso x) (identity_z_iso y) xx yy ≃ @z_iso_disp _ (twosided_disp_cat_to_disp_cat _ _ D) (x ,, y) (x ,, y) (identity_z_iso _) xx yy. Proof. use weq_iso. - exact iso_twosided_disp_to_z_iso_disp. - exact iso_twosided_disp_from_z_iso_disp. - abstract (intros f ; use subtypePath ; [ intro ; apply isaprop_is_iso_twosided_disp | ] ; apply idpath). - abstract (intros f ; use subtypePath ; [ intro ; apply isaprop_is_z_iso_disp | ] ; 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat.