proposition: Lemma is_univalent_LaxMonoidalFunctorCategory' : is_univalent (total_category (functor_monoidal_disp_cat lu luE ru ruE α αE)).
proof: Proof. apply is_univalent_total_category. - apply is_univalent_total_category. + apply (is_univalent_functor_category _ _ Euniv). + apply functor_tensorunit_disp_cat_is_univalent. - apply Constructions.dirprod_disp_cat_is_univalent. { apply Constructions.dirprod_disp_cat_is_univalent. apply functor_lu_disp_cat_is_univalent. apply functor_ru_disp_cat_is_univalent. } apply functor_ass_disp_cat_is_univalent. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.catiso UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedUnitors UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedAssociator