Lemma right_beck_chevalley_nat_trans_comp_ob : right_beck_chevalley_nat_trans P₁ P₃ (fiber_functor_natural_nat_z_iso HD₁ HD₃ (comp_cartesian_disp_functor FF GG) f) a = η₃ _ · #R₃ (fiber_functor_natural_nat_z_iso HD₁ HD₃ (comp_cartesian_disp_functor FF GG) f _) · #R₃ (# (fiber_functor (comp_cartesian_disp_functor FF GG) x) (ε₁ _)). Proof. apply right_beck_chevalley_nat_trans_ob. Qed.
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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Pullbacks.