Lemma adjoint_equivalence_assoc (a b c d : B) (f : adjoint_equivalence a b) (g : adjoint_equivalence b c) (h : adjoint_equivalence c d) : comp_adjoint_equivalence a b d f (comp_adjoint_equivalence b c d g h) = comp_adjoint_equivalence a c d (comp_adjoint_equivalence a b c f g) h. Proof. apply (J_2_0 HB (λ a b f, ∏ (c d : B) (g : adjoint_equivalence b c) (h : adjoint_equivalence c d), comp_adjoint_equivalence a b d f (comp_adjoint_equivalence b c d g h) = comp_adjoint_equivalence a c d (comp_adjoint_equivalence a b c f g) h)). intros. rewrite adjoint_equivalence_lid. apply maponpaths_2. rewrite adjoint_equivalence_lid. 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.