proposition: Lemma ptdptdob_to_ptdob_fmonoidal_laxlaws : fmonoidal_laxlaws ptdptdob_to_ptdob_fmonoidal_data.
proof: Proof. repeat split ; (intro ; intros ; use total2_paths_f ; [ cbn | apply homset_property ]). - rewrite id_left ; apply id_right. - rewrite id_left ; apply id_right. - rewrite (bifunctor_rightid Mon_V). rewrite (bifunctor_leftid Mon_V). rewrite ! id_left. rewrite ! id_right. apply idpath. - rewrite id_right. rewrite (bifunctor_rightid Mon_V). apply id_left. - rewrite id_right. rewrite (bifunctor_leftid Mon_V). apply id_left. Qed.
imports: UniMath.MoreFoundations.All UniMath.Foundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.coslicecat