Definition eq_cartesian_lift_from_adjequiv_transport {B : bicat} (HB : is_univalent_2 B) {D : disp_bicat B} (HD : disp_univalent_2 D) {x y : B} (f : x --> y) (yy : D y) {xx₁ xx₂ : D x} (p : xx₁ = xx₂) (ff : xx₂ -->[ f] yy) : transportb (λ z, z -->[ f ] yy) p ff = transportf (λ z, _ -->[ z ] _) (isotoid_2_1 (pr2 HB) (lunitor_invertible_2cell _)) (disp_idtoiso_2_0 _ (idpath _) _ _ p ;; ff)%mor_disp.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Opposite. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Cartesians. Require Import UniMath.Bicategories.DisplayedBicats.EquivalenceBetweenCartesians.