Definition is_univalent_rel_twosided_disp_cat : is_univalent_twosided_disp_cat rel_disp_cat. Proof. intros X₁ X₂ Y₁ Y₂ p₁ p₂ R₁ R₂. induction p₁, p₂ ; cbn. use weqhomot. - exact (iso_rel_disp_cat R₁ R₂ ∘ rel_weq R₁ R₂)%weq. - abstract (intros p ; induction p ; cbn ; 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.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.