Lemma forget_monoidal_pointed_objects_laxlaws : fmonoidal_laxlaws forget_monoidal_pointed_objects_data. Proof. split5; intro; intros. - rewrite id_left; apply id_right. - rewrite id_left; apply id_right. - do 2 rewrite id_right. cbn. rewrite (bifunctor_leftid Mon_V). rewrite (bifunctor_rightid Mon_V). rewrite id_right; apply id_left. - cbn. rewrite (bifunctor_rightid Mon_V). rewrite id_left. apply id_left. - cbn. rewrite (bifunctor_leftid Mon_V). rewrite id_left. apply id_left. 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.