
theorem Th6:
  for a being R_eal holds Sum<*a*> = a
proof
  let a be R_eal;
  set F = <*a*>;
  consider f being sequence of  ExtREAL such that
A1: Sum F = f.(len F) and
A2: f.0 = 0. and
A3: for i being Nat st i < len F holds f.(i+1) = f.i+F.(i+1)
  by Def2;
A4: f.(0+1) = f.0+F.(0+1) by A3;
  Sum F = f.1 by A1,FINSEQ_1:39;
  then Sum F = F.1 by A2,A4,XXREAL_3:4
    .= a;
  hence thesis;
end;
