proposition: Lemma θ_Strength2_int_nicest_implies_θ_Strength2_int_nicer: θ_Strength2_int_nicest -> θ_Strength2_int_nicer.
proof: Proof. intro Hyp. intros X Z Z'. assert (HypX := Hyp X Z Z'). do 2 rewrite <- assoc. etrans. 2: { apply maponpaths. rewrite assoc. exact HypX. } apply pathsinv0. apply (id_left(a:=functor_compose (U Z ∙ U Z') (H X))). 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