theorem Th10: :: CC0SP2:10

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