
theorem THJ1:
  for Omega being non empty set,
    Sigma being SigmaField of Omega,
    Sigma2 being SigmaField of {1} st
    Omega={1,2,3,4} holds
    ex X1 being Function of Omega,{1} st
     X1 is random_variable of Special_SigmaField1,Sigma2 &
     X1 is random_variable of Special_SigmaField2,Sigma2 &
     X1 is random_variable of Trivial-SigmaField {1,2,3,4},Sigma2
 proof
  let Omega be non empty set;
  let Sigma be SigmaField of Omega;
  let Sigma2 be SigmaField of {1};
  assume A1: Omega={1,2,3,4};
  reconsider 1REAL = 1 as Real;
  consider X1 being Function of Omega,{1REAL} such that F4: X1=Omega-->1REAL;
  reconsider X1 as Function of Omega,{1};
  take X1;
  thus thesis by A1,Lm2A,F4;
 end;
