theorem Th12: :: C0SP1:12

for X being non empty set
for F, G, H being VECTOR of (R_Algebra_of_BoundedFunctions X)
for f, g, h being Function of X,REAL 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) )