theorem Th2: :: CSSPACE2:2

for x, y, z being Point of Complex_l2_Space
for a being Complex holds
( ( x .|. x = 0 implies x = 0. Complex_l2_Space ) & ( x = 0. Complex_l2_Space implies x .|. x = 0 ) & Re (x .|. x) >= 0 & Im (x .|. x) = 0 & x .|. y = (y .|. x) *' & (x + y) .|. z = (x .|. z) + (y .|. z) & (a * x) .|. y = a * (x .|. y) )