Definition left_adjoint_axioms_total_to_base {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 → left_adjoint_axioms (left_adjoint_data_total_to_base td). Proof. intros Hlaw. use tpair. + apply (base_paths _ _ (pr1 Hlaw)). + apply (base_paths _ _ (pr2 Hlaw)). 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.