proposition: Lemma is_univalent_StrongMonoidalFunctorCategory : is_univalent (total_category (functor_strong_monoidal_disp_cat luD luE ruD ruE αD αE)).
proof: Proof. apply is_univalent_total_category. - apply is_univalent_LaxMonoidalFunctorCategory. - apply Constructions.disp_full_sub_univalent. intro ; apply isapropdirprod. apply isaprop_is_nat_z_iso. apply isaprop_is_z_isomorphism. 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