Definition disp_adjoint_equivalence_to_all_invertible_2cell (F₀ : ps_base C D) (F₁ F₁' : map1cells_disp_bicat F₀) : disp_adjoint_equivalence (internal_adjoint_equivalence_identity F₀) F₁ F₁' → (∏ (X Y : C) (f : X --> Y), invertible_2cell (F₁ X Y f) (F₁' X Y f)). Proof. intros m X Y f. use tpair. - refine (rinvunitor _ • _ • lunitor _). exact ((pr1 m X Y f)^-1). - cbn ; is_iso. Defined.
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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Display.Base. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.