Lemma double_transport_compose {C : precategory} {a a' b b' c c' : C} {f : a --> b} {g : b --> c} {px : a = a'} {py : b = b'} {pz : c = c'} : double_transport px py f · double_transport py pz g = double_transport px pz (f · g). Proof. unfold double_transport. destruct px, py, pz. reflexivity. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos.