∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet α cmp} [Std.TransCmp cmp],
  t.isEmpty = false → ∀ {km fallback : α}, t.minD fallback = km ↔ t.get? km = some km ∧ ∀ k ∈ t, (cmp km k).isLE = true