Definition idtoiso_2_0_isotoid_2_0 {B : bicat} (HB : is_univalent_2_0 B) {a b : B} (f : adjoint_equivalence a b) : idtoiso_2_0 _ _ (isotoid_2_0 HB f) = f. Proof. unfold isotoid_2_0. exact (homotweqinvweq (make_weq (idtoiso_2_0 a b) (HB a b)) f). Defined.
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.