theorem Th30: :: C0SP1:30

for X being non empty set
for a being Real
for f, g being Function of X,REAL
for F, G being Point of (R_Normed_Algebra_of_BoundedFunctions X) st f = F & g = G holds
( G = a * F iff for x being Element of X holds g . x = a * (f . x) )