Lemma unique_adjoint_equivalence_inv {a b : B} : ∏ (f : adjoint_equivalence a b), inv_adjequiv f = inv_adjoint_equivalence (pr1 HB) a b f. Proof. use (J_2_0 (pr1 HB) (λ a b f, _)). intro x; simpl. unfold inv_adjoint_equivalence. rewrite J_2_0_comp. use subtypePath. { intro. exact (isaprop_left_adjoint_equivalence _ (pr2 HB)). } apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv.