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