proposition: Lemma δpe'_eq_from_ms: param_distr'_pentagon_eq Mon_V A A' FAm FA'm G δ'_from_ms.
proof: Proof. intros v w. apply param_distr'_pentagon_eq_body_variant_implies. assert (aux := δpe_eq_from_ms(C:=bicat_of_cats) FAm FA'm G sd ms v w). red. etrans. { exact aux. } clear aux. unfold param_distr_bicat_pentagon_eq_body_variant_RHS, param_distr_bicat_pentagon_eq_body_RHS. unfold param_distr'_pentagon_eq_body_variant_RHS. apply (nat_trans_eq A'). intro a. cbn. apply maponpaths. do 3 rewrite id_left. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.MonoidalSections UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfCats