Lemma reindexing_forward_paths_f_mor {a' b':C'} {x' :ob_disp reindexing_forward_ob_mor a'} {y' :ob_disp reindexing_forward_ob_mor b'} {f': C' ⟦ a', b' ⟧} {g': C' ⟦ a', b' ⟧} {p:g'=f'} (Df' : x' -->[ f'] y') (Dg' : x' -->[ g'] y') (e:↙ Dg' = ↙ Df') :← Df' = transportf _ e (← Dg') -> (Df'=transportf _ p Dg'). Proof. intro H. destruct p. exact (! reindexing_forward_mor_eq e (! H)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. 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.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration.