Definition all_invertible_2cell_to_disp_adjoint_equivalence : disp_adjoint_equivalence (internal_adjoint_equivalence_identity F₀) F₁ F₁'. Proof. use tpair. - exact all_invertible_left_adj. - use tpair. + use tpair. * exact all_invertible_right_adj. * split. ** exact all_invertible_unit. ** exact all_invertible_counit. + split ; split. * repeat (apply funextsec ; intro). apply D. * repeat (apply funextsec ; intro). apply D. * apply all_invertible_map1cells. * apply all_invertible_map1cells. 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.