∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Regular C] {X Y : C} (f : X ⟶ Y)
  (this : CategoryTheory.IsIso (CategoryTheory.Regular.strongEpiMonoFactorisation f).m),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Iso.refl
          (CategoryTheory.Arrow.mk (CategoryTheory.Regular.strongEpiMonoFactorisation f).e).left).hom
      (CategoryTheory.Arrow.mk f).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Arrow.mk (CategoryTheory.Regular.strongEpiMonoFactorisation f).e).hom
      (CategoryTheory.asIso (CategoryTheory.Regular.strongEpiMonoFactorisation f).m).hom