theorem Th3: :: C0SP2:3

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 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) )