Lemma univalent_bicategory_1_cell_hlevel_3 (C : bicat) (HC : is_univalent_2_1 C) (a b : C) : isofhlevel 3 (C⟦a,b⟧). Proof. intros f g. apply (isofhlevelweqb _ (idtoiso_2_1 f g,, HC _ _ f g)). apply isaset_invertible_2cell. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.BicategoryLaws.