theorem :: DBLSEQ_3:92

for f being nonnegative Function of [:NAT,NAT:],ExtREAL
for seq being ExtREAL_sequence st ( for m being Element of NAT holds
( ProjMap1 (f,m) is non-decreasing & seq . m = lim (ProjMap1 (f,m)) ) ) holds
( lim_in_cod1 (Partial_Sums_in_cod1 f) is non-decreasing & Sum seq = lim (lim_in_cod1 (Partial_Sums_in_cod1 f)) )