∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [Std.LawfulEqCmp cmp] {he : t ≠ ∅} {km : α}, t.maxKey he = km ↔ km ∈ t ∧ ∀ k ∈ t, (cmp k km).isLE = true