Definition left_equivalence_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_equivalence_axioms td → left_equivalence_axioms (left_adjoint_data_total_to_base td). Proof. intros Hlaw. pose (Hη := pr1 Hlaw). pose (Hε := pr2 Hlaw). use tpair. + apply (is_invertible_total_to_base _ _ Hη). + apply (is_invertible_total_to_base _ _ Hε). 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.