∀ {α : Type u_1} {lb : Option α} {cut : α → Ordering} {x : α} {t : Batteries.RBNode α},
  (∀ {x : α}, x ∈ lb → cut x ≠ Ordering.lt) → Batteries.RBNode.lowerBound? cut t lb = some x → cut x ≠ Ordering.lt