proposition: Lemma is_nat_trans_tensor_comp {F G H : functor C D} (FF : functor_tensor F) (GG : functor_tensor G) (HH : functor_tensor H) {α : nat_trans F G} {β : nat_trans G H} (αα : is_nat_trans_tensor FF GG α) (ββ : is_nat_trans_tensor GG HH β) : is_nat_trans_tensor FF HH (nat_trans_comp _ _ _ α β).
proof: Proof. intros x y. simpl. etrans. { apply maponpaths_2. exact (functor_comp TD (α x #, α y) (β x #, β y)). } rewrite assoc'. etrans. { apply maponpaths. exact (ββ x y). } do 2 rewrite assoc. apply maponpaths_2. apply αα. 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