reserve Omega for set;
reserve X, Y, Z, p,x,y,z for set;
reserve D, E for Subset of Omega;
reserve f for Function;
reserve m,n for Nat;
reserve r,r1 for Real;
reserve seq for Real_Sequence;
reserve F for Field_Subset of X;
reserve ASeq,BSeq for SetSequence of Omega;
reserve A1 for SetSequence of X;
reserve Sigma for SigmaField of Omega;
reserve Si for SigmaField of X;
reserve A, B for Event of Sigma,
  ASeq for SetSequence of Sigma;
reserve P for Function of Sigma,REAL;
reserve Omega for non empty set;
reserve Sigma for SigmaField of Omega;
reserve A, B for Event of Sigma,
  ASeq for SetSequence of Sigma;
reserve P for Function of Sigma,REAL;
reserve D, E for Subset of Omega;
reserve BSeq for SetSequence of Omega;
reserve P for Probability of Sigma;

theorem Th38:
  P.(A \/ B) = P.A + P.B - P.(A /\ B)
proof
  P.(A \/ B) = P.A + P.(B \ (A /\ B)) by Th37
    .= P.A + (P.B - P.(A /\ B)) by Th33,XBOOLE_1:17;
  hence thesis;
end;
