∀ {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], t ≠ ∅ → ∀ {k : α}, (cmp t.maxKey! k).isLE = true ↔ ∀ k' ∈ t, (cmp k' k).isLE = true