theorem Th89: :: PREPOWER:89

for p being Rational
for s1, s2 being Real_Sequence st s1 is convergent & s2 is convergent & lim s1 > 0 & ( for n being Nat holds
( s1 . n > 0 & s2 . n = (s1 . n) #Q p ) ) holds
lim s2 = (lim s1) #Q p