∀ {α : Type u_1} {cmp : α → α → Ordering} {cut : α → Ordering},
  (∀ {x y : α} [Std.TransCmp cmp], cmp x y ≠ Ordering.gt → cut x = Ordering.lt → cut y = Ordering.lt) →
    (∀ {x y : α} [Std.TransCmp cmp], cmp x y ≠ Ordering.gt → cut y = Ordering.gt → cut x = Ordering.gt) →
      Batteries.RBNode.IsCut cmp cut