Karabiner-private.xml for mapping mouse forward/back buttons to next/prev space

private.xml

<?xml version="1.0"?>
<root>
  <item>
    <identifier>private.button_4_next_space</identifier>
    <name>Mouse buttons to move spaces</name>
    <appendix>Mouse button 4 to next space</appendix>
    <autogen>
      __KeyToKey__
      PointingButton::BUTTON4,
      KeyCode::CURSOR_RIGHT, ModifierFlag::COMMAND_L | ModifierFlag::CONTROL_L
    </autogen>
    <appendix>Mouse button 5 to previous space</appendix>
    <autogen>
      __KeyToKey__
      PointingButton::BUTTON5,
      KeyCode::CURSOR_LEFT, ModifierFlag::COMMAND_L | ModifierFlag::CONTROL_L
    </autogen>
  </item>
</root>