reserve Omega for set;
reserve m,n,k for Nat;
reserve x,y for object;
reserve r,r1,r2,r3 for Real;
reserve seq,seq1 for Real_Sequence;
reserve Sigma for SigmaField of Omega;
reserve ASeq,BSeq for SetSequence of Sigma;
reserve A, B, C, A1, A2, A3 for Event of Sigma;
reserve Omega for non empty set;
reserve Sigma for SigmaField of Omega;
reserve A, B, C, A1, A2, A3 for Event of Sigma;
reserve ASeq,BSeq for SetSequence of Sigma;
reserve P,P1,P2 for Probability of Sigma;

theorem Th26:
  A,B are_independent_respect_to P implies ([#] Sigma \ A),([#]
  Sigma \ B) are_independent_respect_to P
proof
  assume A,B are_independent_respect_to P;
  then A,([#] Sigma \ B) are_independent_respect_to P by Th25;
  then ([#] Sigma \ B),A are_independent_respect_to P;
  then ([#] Sigma \ B),([#] Sigma \ A) are_independent_respect_to P by Th25;
  hence thesis;
end;
