∀ (X Y : CategoryTheory.Cat) (x : CategoryTheory.Limits.BinaryFan X Y) (x_1 : x.pt ⟶ CategoryTheory.Cat.of (↑X × ↑Y)),
  CategoryTheory.CategoryStruct.comp x_1 (CategoryTheory.Prod.fst ↑X ↑Y).toCatHom = x.fst →
    CategoryTheory.CategoryStruct.comp x_1 (CategoryTheory.Prod.snd ↑X ↑Y).toCatHom = x.snd →
      x_1 = (x.fst.toFunctor.prod' x.snd.toFunctor).toCatHom