∀ {α : Type u_1} {β : α → Type u_2} {cmp : α → α → Ordering} [inst : Std.TransCmp cmp] (t : Std.ExtDTreeMap α β cmp)
  (k : α),
  (∃ a ∈ t, cmp a k = Ordering.lt) →
    ∀ (m : Std.DTreeMap α β cmp), t = Std.ExtDTreeMap.mk m → ∃ a ∈ Std.ExtDTreeMap.mk m, cmp a k = Ordering.lt