proposition: Lemma strictlytensorpreserving_is_strong {C D : category} {M : monoidal C} {N : monoidal D} {F : functor C D} {pt : preserves_tensordata M N F} (pst : preserves_tensor_strictly pt) : preserves_tensor_strongly pt.
proof: Proof. intros x y. use (iso_stable_under_equalitytransportf (pr2 (pst x y)) (is_z_isomorphism_identity (F x ⊗_{N} F y))). 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.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric