Lemma pathscomp0_disp {C} {D : disp_cat C} {x y} {f f' f'' : x --> y} (e : f' = f) (e' : f'' = f') (e'' : f'' = f) {xx : D x} {yy} (ff : xx -->[f] yy) (ff' : xx -->[f'] yy) (ff'' : xx -->[f''] yy) : (ff = transportf _ e ff') -> (ff' = transportf _ e' ff'') -> ff = transportf _ e'' ff''. Proof. intros ee ee'. etrans. eapply pathscomp0_dep. apply ee. apply ee'. apply maponpaths_2, homset_property. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering.