theorem Th4: :: C0SP2:4

for X being non empty TopSpace
for F, G, H being VECTOR of (R_Algebra_of_ContinuousFunctions X)
for f, g, h being RealMap of X
for a being Real st f = F & g = G holds
( G = a * F iff for x being Element of X holds g . x = a * (f . x) )