Definition disp_left_adjoint_equivalence_fullsubbicat {x y : C} {l : x --> y} (Hl : left_adjoint_equivalence l) {Hx : disp_fullsubbicat x} {Hy : disp_fullsubbicat y} (ll : Hx -->[ l ] Hy) : disp_left_adjoint_equivalence Hl ll. Proof. simple refine ((tt ,, (tt ,, tt)) ,, ((_ ,, _) ,, ((tt ,, (_ ,, _)) ,, (tt ,, (_ ,, _))))) ; apply isapropunit. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. 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. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat.