Definition to_is_twosided_disp_cat_iso_constant (x : C₁) (y : C₂) {z₁ z₂ : D} (f : z₁ --> z₂) (Hf : is_z_isomorphism f) : @is_iso_twosided_disp _ _ constant_twosided_disp_cat _ _ _ _ _ _ _ _ (identity_is_z_iso x) (identity_is_z_iso y) f. Proof. pose (f_iso := (f ,, Hf) : z_iso _ _). simple refine (_ ,, _ ,, _). - exact (inv_from_z_iso f_iso). - abstract (cbn ; unfold transportb_disp_mor2, transportf_disp_mor2 ; cbn ; rewrite !transportf_const ; apply Hf). - abstract (cbn ; unfold transportb_disp_mor2, transportf_disp_mor2 ; cbn ; rewrite !transportf_const ; apply Hf). 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.