∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X E Y YE : C} (c : CategoryTheory.Limits.BinaryCofan X E)
  (hc : CategoryTheory.Limits.IsColimit c) {f : X ⟶ Y} {iY : Y ⟶ YE} {fE : c.pt ⟶ YE},
  CategoryTheory.CommSq f c.inl iY fE →
    (Nonempty
        (CategoryTheory.Limits.IsColimit
          (CategoryTheory.Limits.BinaryCofan.mk (CategoryTheory.CategoryStruct.comp c.inr fE) iY)) ↔
      CategoryTheory.IsPushout f c.inl iY fE)