Lemma postcompWithProductArrow {c : ∏ i, C} (Pc : Product c) {a : ∏ i, C} (Pa : Product a) (f : ∏ i, a i --> c i) {x : C} (k : ∏ i, x --> a i) : ProductArrow Pa k · ProductOfArrows Pc Pa f = ProductArrow Pc (λ i, k i · f i). Proof. apply ProductArrowUnique; intro i. now rewrite <- assoc, ProductOfArrowsPr, assoc, ProductPrCommutes. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.Combinatorics.StandardFiniteSets. Section ProductFromIso. End ProductFromIso.