Proposition ProductArrow_eq {d : I → C} (w : C) (x : Product d) (f g : w --> x) (p : ∏ (i : I), f · ProductPr x i = g · ProductPr x i) : f = g. Proof. refine (ProductArrowEta _ _ _ _ @ _ @ !(ProductArrowEta _ _ _ _)). apply maponpaths. use funextsec. exact p. 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.