Definition disp_left_equivalence_to_left_adjoint_equivalence {B : bicat} {D : disp_bicat B} {x y : B} {f : x --> y} {Hf : left_equivalence f} {xx : D x} {yy : D y} {ff : xx -->[ f ] yy} (Hff : disp_left_equivalence Hf ff) : ∑ (Hf' : left_adjoint_equivalence f), disp_left_adjoint_equivalence Hf' ff := left_adjoint_equivalence_total_disp_weq f ff (pr2 (equiv_to_adjequiv _ (disp_left_equivalence_to_total Hff))).
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.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.Univalence.