∀ {α : Type u_1} {cmp : α → α → Ordering} {cut : α → Ordering} {t : Batteries.RBNode α} {x y : α} [Std.TransCmp cmp]
  [Batteries.RBNode.IsStrictCut cmp cut],
  Batteries.RBNode.Ordered cmp t →
    Batteries.RBNode.lowerBound? cut t = some x → y ∈ t → (cmp x y = Ordering.lt ↔ cut y = Ordering.lt)