proposition: Lemma θ_Strength2_int_nicer_implies_θ_Strength2_int: θ_Strength2_int_nicer -> θ_Strength2_int.
proof: Proof. intro Hyp. intros X Z Z'. assert (HypX := Hyp X Z Z'). set (auxiso := functor_on_z_iso H (z_iso_inv (_,,(lassociator_CAT_pointwise_is_z_iso (U Z) (U Z') X)))). apply (z_iso_inv_to_right _ _ _ _ auxiso). assumption. Qed.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.Notation