 reserve Omega for non empty set;
 reserve F for SigmaField of Omega;

theorem Lemma00:
  for f,RV being random_variable of F,Borel_Sets,
      K being Real holds
    (f-RV)"[.0,+infty.[ is Element of F
  proof
    let f,RV be random_variable of F,Borel_Sets,
        K be Real;
A1: [.0,+infty.[ is Element of Borel_Sets by FINANCE1:3;
    f-RV is (F,Borel_Sets)-random_variable-like by FINANCE2:24;
    hence thesis by A1;
  end;
