Definition sectionfunctor_preservestensorstrongly {sd : section_disp D} {ms : smonoidal sd} (pfstrong : smonoidal_strongtensor (smonoidal_preserves_tensor ms)) : preserves_tensor_strongly (sectionfunctor_preserves_tensordata (smonoidal_preserves_tensor ms)). Proof. intros x y. use tpair. - use tpair. + apply identity. + exact (pr1 (pfstrong x y)). - use tpair. + use total2_paths_b. * apply id_left. * apply (pr2 (pr2 (pfstrong x y))). + use total2_paths_b. * apply id_left. * apply (pr1 (pr2 (pfstrong x y))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.