∀ {J : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} J] (F : CategoryTheory.Functor J CommMonCat)
  (x : CategoryTheory.Limits.Cone F)
  (v : ((CategoryTheory.forget MonCat).mapCone ((CategoryTheory.forget₂ CommMonCat MonCat).mapCone x)).pt) {j j' : J}
  (f : j ⟶ j'),
  CategoryTheory.CategoryStruct.comp
      (((CategoryTheory.forget MonCat).mapCone ((CategoryTheory.forget₂ CommMonCat MonCat).mapCone x)).π.app j)
      (((F.comp (CategoryTheory.forget₂ CommMonCat MonCat)).comp (CategoryTheory.forget MonCat)).map f) v =
    ((CategoryTheory.forget MonCat).mapCone ((CategoryTheory.forget₂ CommMonCat MonCat).mapCone x)).π.app j' v