∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
  {k : α}, (∀ (k' : α), t.minKey? = some k' → (cmp k k').isLE = true) ↔ ∀ k' ∈ t, (cmp k k').isLE = true