∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [Std.TransCmp cmp] {k : α} {v : β}
  {fallback : α}, (t.insert k v).minKeyD fallback = t.minKey?.elim k fun k' => if (cmp k k').isLE = true then k else k'