∀ {J : Type w} [inst : CategoryTheory.Category.{w', w} J] [CategoryTheory.IsConnected J] {C : Type u}
  [inst_2 : CategoryTheory.Category.{v, u} C] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_4 : CategoryTheory.Limits.HasPushouts C] [inst_5 : CategoryTheory.Limits.HasLimitsOfShape J C]
  [CategoryTheory.HasExactLimitsOfShape J C] {F : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cone F}
  (hc : CategoryTheory.Limits.IsLimit c) {X Y : C} {g : Y ⟶ c.pt} {f : c.pt ⟶ X},
  (∀ (j : J),
      CategoryTheory.CategoryStruct.comp g
          (CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.pushout.inr (c.π.app j) f)) =
        0) →
    CategoryTheory.CategoryStruct.comp g f = 0