Lemma is_nat_trans_product_nat_trans_data : is_nat_trans _ _ product_nat_trans_data. Proof. intros a b k; simpl. eapply pathscomp0; [apply precompWithProductArrow|]. apply pathsinv0. eapply pathscomp0; [apply postcompWithProductArrow|]. apply maponpaths, funextsec; intro i. now rewrite (nat_trans_ax (f 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.