Lemma transport_source_precompose {C : precategory} {x y z w : ob C} (f : x --> y) (g : y --> z) (e : x = w) : transportf (λ x' : ob C, precategory_morphisms x' z) e (f · g) = transportf (λ x' : ob C, precategory_morphisms x' y) e f · g. Proof. induction e. apply idpath. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos.