∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [Std.TransCmp cmp],
  t.isEmpty = false →
    ∀ {k : α} {v : β} {fallback : α}, (cmp ((t.insert k v).minKeyD fallback) (t.minKeyD fallback)).isLE = true