theorem Th31: :: C0SP1:31

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