Definition eq_cartesian_lift_from_adjequiv {B : bicat} (HB : is_univalent_2 B) (D : disp_bicat B) (HD : disp_univalent_2 D) {x y : B} {yy : D y} {f : x --> y} (ℓ₁ ℓ₂ : ∑ (xx : D x) (ff : xx -->[ f ] yy), cartesian_1cell D ff) (e : disp_adjoint_equivalence (internal_adjoint_equivalence_identity x) (pr1 ℓ₁) (pr1 ℓ₂)) (γ : disp_invertible_2cell (lunitor_invertible_2cell _) (e ;; pr12 ℓ₂) (pr12 ℓ₁)) : ℓ₁ = ℓ₂.
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.