reserve x,y for object,
        D,D1,D2 for non empty set,
        i,j,k,m,n for Nat,
        f,g for FinSequence of D*,
        f1 for FinSequence of D1*,
        f2 for FinSequence of D2*;
reserve f for complex-valued Function,
        g,h for complex-valued FinSequence;

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;
