Definition disp_psfunctor_id_on_disp_adjequiv {B : bicat} {D₁ D₂ : disp_bicat B} (FF : disp_psfunctor D₁ D₂ (id_psfunctor _)) {x y : B} {f : adjoint_equivalence x y} {xx : D₁ x} {yy : D₁ y} {ff : xx -->[ f ] yy} (Hff : disp_left_adjoint_equivalence f ff) : disp_left_adjoint_equivalence _ (disp_psfunctor_mor _ _ _ FF ff) := pr2 (left_adjoint_equivalence_total_disp_weq _ _ (psfunctor_preserves_adjequiv' (total_psfunctor _ _ _ FF) (invmap (left_adjoint_equivalence_total_disp_weq f ff) (pr2 f ,, Hff)))).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. 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.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.FiberCategory. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Import PseudoFunctor.Notations.