Lemma right_beck_chevalley_nat_trans_comp_ob_on_right : right_beck_chevalley_nat_trans P₂ P₃ (fiber_functor_natural_nat_z_iso HD₂ HD₃ GG (#F f)) (FF x a) = η₃ _ · #R₃ (fiber_functor_natural_nat_z_iso HD₂ HD₃ GG (#F f) _) · #R₃ (# (fiber_functor GG (F x)) (ε₂ _)). 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.