These lines are shown only for the group group_no_one.  They help compute in Sale Order the quantity invoiced.  Standard invoice increase and  a refund automatically decrease the invoiced quantity. In general, it is convenient to see, what has been invoiced.

Example:
Step 1. Create invoice - Partner ABC - without Sale Order
Product Service XYZ * 5 PCE * 100 USD
Step 2. Create and confirm Sale order - Partner ABC
Product Service XYZ * 3 PCE * 100 USD
Step 3. Invoice this SO.
Step 4. See invoice lines in SO
Step 5. Edit confirmed SO and change ordered quantity to 9, and look at invoiced quantity = 3
Step 6. Edit SO and line. Select now and add (in invoiced lines) values/line from first step
Step 7. Look now at invoiced quantity = 8