∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} {c : CategoryTheory.Limits.BinaryFan X Y}
  (hc : CategoryTheory.Limits.IsLimit c) (x : CategoryTheory.Limits.BinaryCofan (Opposite.op X) (Opposite.op Y)),
  (CategoryTheory.CategoryStruct.comp c.fst.op ((fun s => (hc.lift s.unop).op) x)).unop = x.inl.unop