Definition ptdob_to_ptdptdob_fmonoidal_stronglaws : fmonoidal_stronglaws (fmonoidal_preservestensordata ptdob_to_ptdptdob_fmonoidal_lax) (fmonoidal_preservesunit ptdob_to_ptdptdob_fmonoidal_lax). Proof. split; ( (try intro ; intros) ; repeat (use tpair) ; [ exact (identity _) | apply id_right | abstract (use total2_paths_f ; [ apply id_right | apply homset_property ]) | abstract ( use total2_paths_f ; [ use total2_paths_f ; [apply id_right | apply V] | apply homset_property ] ) | abstract ( use total2_paths_f ; [ use total2_paths_f ; [apply id_right | apply V] | 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.