Definition from_iso_rel_disp_cat {X Y : SET} (R₁ R₂ : rel_disp_cat X Y) (f : iso_twosided_disp (identity_z_iso X) (identity_z_iso Y) R₁ R₂) : ∏ (x : pr1 X) (y : pr1 Y), (R₁ x y → R₂ x y) × (R₂ x y → R₁ x y) := λ x y, pr1 f x y ,, pr12 f x y.
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.Categories.HSET.Core. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedFibration.