theorem Th8:
  for A,B being non empty Subset of Sigma st A c= Indep(B,P) holds
  B c= Indep(A,P)
proof
  let A, B be non empty Subset of Sigma;
  assume
A1: A c= Indep(B,P);
  for q,p st q in B & p in A holds q,p are_independent_respect_to P
      by A1,Th7,PROB_2:19;
  hence thesis by Th7;
end;
