Definition disp_alg_bicat_univalent_2_1 : disp_univalent_2_1 disp_alg_bicat. Proof. intros a b f g p aa bb ff gg. induction p. apply isweqimplimpl. - cbn. intros x. pose (pr1 x) as d. cbn in *. unfold alg_disp_cat_2cell in *. rewrite lwhisker_id2 in d. rewrite id2_left in d. rewrite psfunctor_id2 in d. rewrite id2_rwhisker in d. rewrite id2_right in d. use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } exact (!d). - apply isaset_invertible_2cell. - apply disp_alg_bicat_disp_invertible_2cell. 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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.