∀ {α : Type u} {instOrd : Ord α} {β : Type v} {t : Std.DTreeMap.Internal.Impl α fun x => β} [Std.TransOrd α]
  [inst : Inhabited α],
  t.WF →
    ∀ {k : α} {f : Option β → Option β},
      (Std.DTreeMap.Internal.Impl.Const.alter! k f t).isEmpty = false →
        ((Std.DTreeMap.Internal.Impl.Const.alter! k f t).minKey! = k ↔
          (f (Std.DTreeMap.Internal.Impl.Const.get? t k)).isSome = true ∧ ∀ k' ∈ t, (compare k k').isLE = true)