 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 T:
  for Omega,Omega2 be non empty set
  for F be SigmaField of Omega
  for F2 be SigmaField of Omega2
  for k be Element of set_of_random_variables_on(F,F2) holds
  Change_Element_to_Func(F,F2,k) is random_variable of F,F2
proof
  let Omega,Omega2 be non empty set;
  let F be SigmaField of Omega;
  let F2 be SigmaField of Omega2;
  let k be Element of set_of_random_variables_on(F,F2);
  Change_Element_to_Func(F,F2,k) is Element of
     {f where f is Function of Omega,Omega2:
     f is (F,F2)-random_variable-like} by FINANCE1:def 7;
  then Change_Element_to_Func(F,F2,k) in
     {f where f is Function of Omega,Omega2:
     f is (F,F2)-random_variable-like}; then
  ex Y being Function of Omega,Omega2 st
     Change_Element_to_Func(F,F2,k)=Y & Y is (F,F2)-random_variable-like;
  hence thesis;
end;
