
theorem Th33:
for a be R_eal holds Sum <*a*> = a
proof
   let a be R_eal;
   consider f be sequence of ExtREAL such that
A1: Sum <*a*> = f.(len <*a*>) & f.0 = 0. &
    for i be Nat st i < len <*a*> holds f.(i+1) = f.i+ <*a*>.(i+1)
      by EXTREAL1:def 2;
A2:len <*a*> = 1 by FINSEQ_1:39;
   f.(0+1) = f.0 + <*a*>.(0+1) by A1
    .= 0 + a by A1;
   hence Sum <*a*> = a by A1,A2,XXREAL_3:4;
end;
