Proposition idtoisotoid_twosided_disp {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} (HD : is_univalent_twosided_disp_cat D) {x₁ x₂ : C₁} {y₁ y₂ : C₂} (p : x₁ = x₂) (q : y₁ = y₂) {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} (r : transportf (λ z, D z _) p (transportf (λ z, D _ z) q xy₁) = xy₂) : isotoid_twosided_disp HD p q (idtoiso_twosided_disp p q r) = r. Proof. apply homotinvweqweq. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos.