proposition: Lemma is_nat_trans_product_nat_trans_data : is_nat_trans _ _ product_nat_trans_data.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.Combinatorics.StandardFiniteSets