theorem Th11: :: CC0SP2:11

for X being non empty TopSpace
for F, G being VECTOR of (C_Algebra_of_ContinuousFunctions X)
for f, g being Function of the carrier of X,COMPLEX
for a being Complex st f = F & g = G holds
( G = a * F iff for x being Element of X holds g . x = a * (f . x) )