∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp] {k : α}
  {v : β}, (t.insertIfNew k v).minKey ⋯ = t.minKey?.elim k fun k' => if cmp k k' = Ordering.lt then k else k'