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