Proposition is_univalent_ver_cyl_twosided_disp_cat : is_univalent_twosided_disp_cat ver_cyl_twosided_disp_cat. Proof. intros u₁ u₂ v₁ v₂ p₁ p₂ s₁ s₂. induction p₁, p₂ ; cbn. use isweqimplimpl. - intros f. pose (p := pr1 f) ; cbn in p. rewrite lwhisker_square_id in p. rewrite rwhisker_square_id in p. exact (!p). - apply isaset_square_double_bicat. - use isaproptotal2. + intro. apply isaprop_is_iso_twosided_disp. + intros. apply isaset_square_double_bicat. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. 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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws.