theorem :: NEWTON05:56

for a, b being Integer holds
( parity (a + b) = ((parity a) + (parity b)) - ((2 * (parity a)) * (parity b)) & (parity a) - (parity b) = (parity (a + b)) - ((2 * (parity (a + b))) * (parity b)) & (parity a) - (parity b) = ((2 * (parity a)) * (parity (a + b))) - (parity (a + b)) )