∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [inst_1 : Inhabited α] {k : α} {v : β k},
  (t.insert k v).minKey! = t.minKey?.elim k fun k' => if (cmp k k').isLE = true then k else k'