∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp] {k : α},
  (∀ {km : α}, t.minKey? = some km → ¬cmp k km = Ordering.eq) → (t.erase k).minKey? = t.minKey?