Lemma isaprop_disp_left_adjoint_data_cell_unit_bicat {C : bicat} {D : disp_cat_data C} {a b : C} {f : C⟦ a, b ⟧} (l : left_adjoint_data f) {aa : (disp_cell_unit_bicat D) a} {bb : (disp_cell_unit_bicat D) b} (ff : aa -->[ f] bb) : isaprop (bb -->[ left_adjoint_right_adjoint l] aa) -> isaprop (disp_left_adjoint_data l ff). Proof. intro p. use isaproptotal2. - intro ; apply isapropdirprod ; apply isapropunit. - intro ; intros ; apply 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.