Lemma adjoint_equivalence_rinv (a b : B) (f : adjoint_equivalence a b) : comp_adjoint_equivalence a b a f (inv_adjoint_equivalence a b f) = internal_adjoint_equivalence_identity a. Proof. apply (J_2_0 HB (λ a b f, comp_adjoint_equivalence a b a f (inv_adjoint_equivalence a b f) = internal_adjoint_equivalence_identity a)). intro c. rewrite adjoint_equivalence_lid. unfold inv_adjoint_equivalence. rewrite J_2_0_comp. exact (idpath _). 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.