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
  for P,A,B st 0 < P.B holds (P.A + P.B - 1)/ P.B <= P.|.B.A
proof
  let P,A,B such that
A1: 0 < P.B;
  (P.A + P.B - 1)/P.B <= P.(A /\ B)/P.B by A1,Th15,XREAL_1:72;
  hence thesis by A1,Def6;
end;
