Prototype CSS selector to descend tree?

Hi, I'm calling on those with Prototype/CSS selector foo to help with a
somewhat tricky issue.

I have a tree structure where each item is hierarchical. This is used
to manage software components. Think of the case where you're
installing a piece of software, and want to customize which packages
are installed:

[ ] Internet
    [ ] Email
        [ ] Thunderbird
        [ ] Evolution
        [ ] Outlook Express
    [ ] Browsing
        [ ] Firefox
        [ ] Internet Explorer
  [ ] Entertainment
    [ ] Music
        [ ] iTunes
        [ ] Winamp

In this menu, if the user clicks on a given checkbox, I want all sub
elements to check as well (and the same on uncheck, obviously).

Since there are all simple checkboxes, I tried attaching this function
to onclick:

   function toggle_children (input) {
    // locate "input#myid input" (all children)
    $$('input#'' input').each(function (item) {
        if ( !== {
          item.checked = input.checked;

But unfortunately, that did not select the elements. The pure CSS
selector that should work is:

   input#myid > input

However, unfortunately passing that to Prototype gives "error parsing
selector at: > "