theorem
  for X,Y being random_variable of Sigma,Borel_Sets holds
    X+Y is random_variable of Sigma, Borel_Sets
proof
  let X,Y be random_variable of Sigma, Borel_Sets;
  reconsider X,Y as Real-Valued-Random-Variable of Sigma by RANDOM_3:9;
  X+Y is Real-Valued-Random-Variable of Sigma;
  hence thesis by RANDOM_3:9;
end;
