proposition: Lemma LiftPreservesPostTensor : nat_z_iso (H ∙ I_posttensor TD (H I)) (I_posttensor TC I ∙ H).
proof: Proof. use nat_z_iso_comp. 2: { apply pre_whisker_nat_z_iso. apply tensor_after_pair_with_object_right. } use nat_z_iso_comp. 3: { apply nat_z_iso_inv. use post_whisker_nat_z_iso. 2: apply tensor_after_pair_with_object_right. } use nat_z_iso_comp. 3: { apply nat_z_iso_functor_comp_assoc. } use nat_z_iso_comp. 3: { apply pre_whisker_nat_z_iso. exact (TransportedTensorComm Duniv H_eso H_ff TC). } use nat_z_iso_comp. 2: { apply nat_z_iso_functor_comp_assoc. } use nat_z_iso_comp. 3: { apply (nat_z_iso_inv (nat_z_iso_functor_comp_assoc _ _ _)). } apply post_whisker_nat_z_iso. apply PairingWithObjectCommutesRight. Defined.
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.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.catiso UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit