for n being Element of NAT
for x0 being Real
for f1 being PartFunc of REAL,(REAL n)
for f2 being PartFunc of (REAL n),REAL st x0 in dom (f2 * f1) & f1 is_continuous_in x0 & f2 is_continuous_in f1 /. x0 holds
f2 * f1 is_continuous_in x0