Lemma ptdob_to_ptdptdob_fmonoidal_laxlaws : fmonoidal_laxlaws ptdob_to_ptdptdob_fmonoidal_data. Proof. repeat split ; (intro ; intros ; use total2_paths_f ; [ use total2_paths_f ; cbn | apply homset_property ]). - rewrite id_left ; apply id_right. - apply homset_property. - rewrite id_left ; apply id_right. - apply homset_property. - rewrite (bifunctor_rightid Mon_V). rewrite (bifunctor_leftid Mon_V). rewrite ! id_left. rewrite ! id_right. apply idpath. - apply homset_property. - rewrite id_right. rewrite (bifunctor_rightid Mon_V). apply id_left. - apply homset_property. - rewrite id_right. rewrite (bifunctor_leftid Mon_V). apply id_left. - apply homset_property. Qed.
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.