proposition: Lemma Flat_θ_strength2_int: θ_Strength2_int Flat_θ.
proof: Proof. intros ? ? ?. apply nat_trans_eq_alt. intro c. cbn. repeat rewrite id_left. rewrite id_right. repeat rewrite <- functor_comp. apply maponpaths. repeat rewrite functor_id. rewrite id_right. set (c' := pr1 X (pr1 Z' (pr1 Z c))). change (pr1 (ptd_pt C Z) c' · pr1 (ptd_pt C Z') (pr1 (pr1 (pr1 Z)) c') = pr1 (pr2 Z') c' · # (pr1 Z') (pr1 (pr2 Z) c')). etrans. 2: { apply (nat_trans_ax (pr2 Z')). } apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.CategoryTheory.PrecategoryBinProduct UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.BinSumOfSignatures UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits