
theorem Th45:
for seq be ExtREAL_sequence st seq is summable holds -seq is summable
proof
   let seq be ExtREAL_sequence;
   assume seq is summable; then
A1:Partial_Sums seq is convergent by MESFUNC9:def 2;
   (Partial_Sums(-seq)) = -(Partial_Sums seq) by Th44;
   hence -seq is summable by A1,DBLSEQ_3:17,MESFUNC9:def 2;
end;
