theorem Th45:
  for f be complex-valued FinSequence holds
    Sum <*f*> = <*Sum f*>
proof
  let f be complex-valued FinSequence;
  A1:len <*f*> = 1 & dom <*f*>= dom Sum <*f*> & dom <*f*> = Seg 1
    by Def8,FINSEQ_1:39,38;
  A2:(Sum <*f*>).1 = Sum (<*f*>.1) by Def8;
  thus thesis by A1,FINSEQ_3:29,A2,FINSEQ_1:40;
end;
