theorem
  for E being finite non empty set, A,B being Event of E holds prob(A) -
  prob(B) <= prob(A \ B)
proof
  let E be finite non empty set, A,B be Event of E;
  prob(A /\ B) <= prob(B) by Th19,XBOOLE_1:17;
  then prob(A) - prob(B) <= prob(A) - prob(A /\ B) by XREAL_1:13;
  hence thesis by Th23;
end;
