∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap.Raw α β cmp} [Std.TransCmp cmp]
  [inst : Std.LawfulEqCmp cmp] [inst_1 : Inhabited α],
  t.WF →
    ∀ {k : α} {f : Option (β k) → Option (β k)},
      (t.alter k f).isEmpty = false →
        ((t.alter k f).minKey! = k ↔ (f (t.get? k)).isSome = true ∧ ∀ k' ∈ t, (cmp k k').isLE = true)