 reserve Exx for Real;
 reserve Omega,Omega2 for non empty set;
 reserve Sigma for SigmaField of Omega;
 reserve Sigma2 for SigmaField of Omega2;
 reserve X,Y,Z for Function of Omega,REAL;

theorem
  for p be Nat
  for Omega, Omega2 be non empty set
  for F be SigmaField of Omega
  for F2 be SigmaField of Omega2
  for G be sequence of set_of_random_variables_on(F,F2) holds
   Element_Of(F,F2,G,p) is random_variable of F,F2
  proof
  let p be Nat;
  let Omega, Omega2 be non empty set;
  let F be SigmaField of Omega;
  let F2 be SigmaField of Omega2;
  let G be sequence of set_of_random_variables_on(F,F2);
  G.p in set_of_random_variables_on(F,F2); then
  consider Y being Function of Omega,Omega2 such that
A2: G.p=Y & Y is (F,F2)-random_variable-like;
    Element_Of(F,F2,G,p)=Y by FINANCE1:def 9,A2;
    hence thesis by A2;
end;
