theorem Th32: :: VFUNCT_2:32

for M being non empty set
for V being ComplexNormSpace
for f1, f2 being PartFunc of M,V holds
( ( f1 is total & f2 is total implies f1 + f2 is total ) & ( f1 + f2 is total implies ( f1 is total & f2 is total ) ) & ( f1 is total & f2 is total implies f1 - f2 is total ) & ( f1 - f2 is total implies ( f1 is total & f2 is total ) ) )