∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp] {k k' : α}
  {f : β → β} {hc : k' ∈ t.modify k f}, (t.modify k f)[k'] = if heq : cmp k k' = Ordering.eq then f t[k] else t[k']