Lemma ProductArrowUnique (c : ∏ i, C) (P : Product c) (x : C) (f : ∏ i, x --> c i) (k : x --> P) (Hk : ∏ i, k · ProductPr P i = f i) : k = ProductArrow P f. Proof. set (H' := pr2 (isProduct_Product P _ f) (k,,Hk)). apply (base_paths _ _ H'). 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.