proposition: Lemma nat_trans_tensor_ntrans1_is_nat_trans : is_nat_trans (functor_tensor_map_dom TD F) (functor_tensor_map_codom TC G) (λ cc : C × C, # TD (α (pr1 cc) #, α (pr2 cc)) · GG cc).
proof: Proof. intros cc1 cc2 ff. simpl. rewrite assoc. rewrite <- (functor_comp TD). rewrite <- binprod_comp. do 2 rewrite (pr2 α). rewrite binprod_comp. rewrite (functor_comp TD). do 2 rewrite assoc'. apply maponpaths. apply (pr2 GG). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored