proposition: Lemma sectionfunctor_preserves_tensor_nat_right {sd : section_disp D} {spt : section_preserves_tensor_data sd} (sptnl : section_preserves_tensor_nat_right spt) : preserves_tensor_nat_right (sectionfunctor_preserves_tensordata spt).
proof: Proof. intros x1 x2 y f. use total2_paths_b. - cbn. rewrite id_left. apply id_right. - cbn. rewrite sptnl. apply transportb_transpose_left. rewrite transport_f_b. apply pathsinv0. apply transportf_set. apply homset_property. 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.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions