proposition: Lemma θ_Strength2_int_nicer_implies_θ_Strength2_int_nicest: θ_Strength2_int_nicer -> θ_Strength2_int_nicest.
proof: Proof. intro Hyp. intros X Z Z'. assert (HypX := Hyp X Z Z'). etrans. { exact HypX. } etrans. { do 2 apply cancel_postcomposition. apply (id_left(a:=functor_compose (U Z ∙ U Z') (H X))). } apply idpath. 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