Lemma ProductOfArrowsPr {c : ∏ i, C} (Pc : Product c) {a : ∏ i, C} (Pa : Product a) (f : ∏ i, a i --> c i) : ∏ i, ProductOfArrows Pc Pa f · ProductPr Pc i = ProductPr Pa i · f i. Proof. unfold ProductOfArrows; intro i. now rewrite (ProductPrCommutes _ _ _ _ i). 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.