
theorem Th44:
  for seq be ExtREAL_sequence holds Partial_Sums(-seq) = -(Partial_Sums seq)
proof
   let seq be ExtREAL_sequence;
   now let n be Element of NAT;
A1: dom(-(Partial_Sums seq)) = NAT by FUNCT_2:def 1;
    (Partial_Sums(-seq)).n = -((Partial_Sums seq).n) by Th43;
    hence (Partial_Sums(-seq)).n = (-(Partial_Sums seq)).n
      by A1,MESFUNC1:def 7;
   end;
   hence (Partial_Sums(-seq)) = -(Partial_Sums seq) by FUNCT_2:def 8;
end;
