proposition: Lemma is_nat_trans_tensor_id {F : functor C D} (FF : functor_tensor F) : is_nat_trans_tensor FF FF (nat_trans_id F).
proof: Proof. intros x y. simpl. rewrite (functor_id TD). exact (id_left _ @ ! id_right _). 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