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