Definition left_adjoint_axioms_total_to_disp {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)) (ta : left_adjoint_axioms td) : ∑ (ba : left_adjoint_axioms _), disp_left_adjoint_axioms (_,, ba) (left_adjoint_data_total_to_fiber td). Proof. exists (left_adjoint_axioms_total_to_base ta). apply left_adjoint_axioms_total_to_fiber. 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.