Lemma isaprop_disp_adjoint_equivalence_cell_unit_bicat {C : bicat} {D : disp_cat_data C} {a b : C} {aa : (disp_cell_unit_bicat D) a} {bb : (disp_cell_unit_bicat D) b} {f : adjoint_equivalence a b} (ff : aa -->[ f ] bb) : isaprop (bb -->[left_adjoint_right_adjoint f] aa) -> isaprop (aa -->[ f] bb) -> isaprop (disp_adjoint_equivalence f aa bb). Proof. exact (λ p q, isaprop_total2 (_,,q) (λ _ , _ ,, isaprop_disp_left_adjoint_equivalence_cell_unit_bicat _ _ p)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.