∀ {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] [inst_2 : Inhabited α] {k k' : α} {f : Option (β k) → Option (β k)},
  (t.alter k f).getKey! k' =
    if cmp k k' = Ordering.eq then if (f (t.get? k)).isSome = true then k else default else t.getKey! k'