Lemma right_beck_chevalley_nat_trans_comp_ob_on_left : right_beck_chevalley_nat_trans P₁ P₂ (fiber_functor_natural_nat_z_iso HD₁ HD₂ FF f) a = η₂ _ · #R₂ (fiber_functor_natural_nat_z_iso HD₁ HD₂ FF f _) · #R₂ (# (fiber_functor FF 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.