theorem Th80: :: DBLSEQ_3:80

for f being nonnegative Function of [:NAT,NAT:],ExtREAL st Partial_Sums f is convergent_in_cod1_to_finite holds
for m being Element of NAT holds (Partial_Sums (lim_in_cod1 (Partial_Sums_in_cod1 f))) . m = lim (ProjMap2 ((Partial_Sums_in_cod1 (Partial_Sums_in_cod2 f)),m))