Definition final_bicat_is_univalent_2_1 : is_univalent_2_1 final_bicat. Proof. intros x y p q. use isweqimplimpl. - intros. apply isasetaprop. apply isapropunit. - apply isasetaprop. apply isasetaprop. exact isapropunit. - simple refine (isaprop_total2 (_ ,, _) (λ η , _ ,, _)). + exact isapropunit. + apply isaprop_is_invertible_2cell. Defined.
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.Categories.StandardCategories. 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.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique.