∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [inst_1 : Std.LawfulEqCmp cmp] {k : α} {f : Option (β k) → Option (β k)} {he : t.alter k f ≠ ∅},
  (t.alter k f).maxKey he = k ↔ (f (t.get? k)).isSome = true ∧ ∀ k' ∈ t, (cmp k' k).isLE = true