Definition left_adjoint_axioms_total_weq {a b : B} {aa : D a} {bb : D b} {f : a --> b} {ff : aa -->[f] bb} (td : @left_adjoint_data E (a,,aa) (b,,bb) (f,,ff)): left_adjoint_axioms td ≃ ∑ (ba : left_adjoint_axioms _), disp_left_adjoint_axioms (_,, ba) (left_adjoint_data_total_to_fiber td). Proof. apply weqimplimpl. - exact (left_adjoint_axioms_total_to_disp td). - exact (left_adjoint_axioms_disp_to_total td). - apply isofhleveltotal2; try intro; apply cellset_property. - apply isofhleveltotal2. { apply isofhleveltotal2; try intro; apply cellset_property. } intro. apply isofhleveltotal2; try intro; apply disp_cellset_property. Defined.
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.