Definition ptdptdob_to_ptdob_fmonoidal_stronglaws : fmonoidal_stronglaws (fmonoidal_preservestensordata ptdptdob_to_ptdob_fmonoidal_lax) (fmonoidal_preservesunit ptdptdob_to_ptdob_fmonoidal_lax). Proof. split ; ( (try intro ; intros) ; repeat (use tpair) ; [ exact (identity _) | abstract (apply id_right) | abstract (use total2_paths_f ; [ apply id_right | apply homset_property ]) | abstract (use total2_paths_f ; [ apply id_right | apply homset_property ]) ]). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Foundations.PartA. 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.coslicecat. Import BifunctorNotations. Import MonoidalNotations.