∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp]
  [inst : Inhabited α] {k : α}, (t.erase k).isEmpty = false → (cmp t.minKey! (t.erase k).minKey!).isLE = true