Definition functorlifting_preservestensorstrongly {Fs : preserves_tensor_strongly (fmonoidal_preservestensordata Fm)} {ms : flmonoidal_lax} (pfstrong : fl_strongtensor (flmonoidal_preserves_tensor_data ms) Fs) : preserves_tensor_strongly (functorlifting_preserves_tensordata (flmonoidal_preserves_tensor_data ms)). Proof. intros x y. use tpair. - exists (pr1 (Fs x y)). exact (pr1 (pfstrong x y)). - use tpair. + use total2_paths_b. * exact (pr12 (Fs x y)). * exact (pr22 (pfstrong x y)). + use total2_paths_b. * exact (pr22 (Fs x y)). * exact (pr12 (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.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.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.