Where do you get this stuff from?
Since you quoted my quotes back at me I thought that was obvious
A CPL or ATPL include the privileges of a PPL
Only if the CPL or ATPL is valid (otherwise no privileges exist at all)
The medical required must match the privileges you are exercising
Part-Med.A.030 and FCL.040 are EU Law and say exactly that
NO THEY DON'T - Read the quotes again.
Part-Med.A.030 says what medical is required to hold a
Licence.
FCL.040 says that a medical must be valid (not what class of medical)