Lemma isaprop_left_adjoint_equivalence {C : bicat} {X Y : C} (f : X --> Y) : is_univalent_2_1 C → isaprop (left_adjoint_equivalence f). Proof. intros HU. apply invproofirrelevance. intros A1 A2. apply unique_internal_adjoint_equivalence. assumption. 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.