 reserve Omega for non empty set;
 reserve r for Real;
 reserve Sigma for SigmaField of Omega;
 reserve P for Probability of Sigma;

theorem Th9:
  for DX be non empty set, F be Function of DX,REAL,
  Y be finite Subset of DX holds
  ex p being FinSequence of DX st p is one-to-one &
  rng p = Y & setopfunc(Y,DX,REAL,F,addreal)=Sum(Func_Seq(F,p))
  proof
    let DX be non empty set,
    F be Function of DX,REAL,
    Y be finite Subset of DX;
    consider p being FinSequence of DX such that
    A1: p is one-to-one & rng p = Y & setopfunc(Y,DX,REAL,F,addreal)
    = (addreal) "**" Func_Seq(F,p) by BHSP_5:def 5;
    Sum(Func_Seq(F,p)) = (addreal) "**" Func_Seq(F,p);
    hence thesis by A1;
  end;
