theorem TH12: :: ASYMPT_3:21

for f, h being VECTOR of R_Algebra_of_Big_Oh_poly
for f9, h9 being Function of NAT,REAL st f9 = f & h9 = h holds
for a being Real holds
( h = a * f iff for x being Nat holds h9 . x = a * (f9 . x) )