Definition path_right_adjoint_over_id_data_help {C : category} {D₁ D₂ : disp_cat C} {F : disp_functor (functor_identity C) D₁ D₂} {HF₁ HF₂ : right_adjoint_over_id_data F} (p₁ : pr1 HF₁ = pr1 HF₂) (p₂ : ∏ (x : C) (xx : D₁ x), pr12 HF₁ x xx ;; idtoiso_disp (idpath _) (maponpaths (λ z, pr11 z x (F x xx)) p₁) = transportf (λ z, _ -->[ z ] _) (!(id_right _)) (pr12 HF₂ x xx)) (p₃ : ∏ (x : C) (xx : D₂ x), pr22 HF₁ x xx = transportf (λ z, _ -->[ z ] _) (id_left _) (♯F (idtoiso_disp (idpath _) (maponpaths (λ z, pr11 z x xx) p₁)) ;; pr22 HF₂ x xx)) : HF₁ = HF₂.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq.