reserve E for non empty set;
reserve a for Element of E;
reserve A, B for Subset of E;
reserve Y for set;
reserve p for FinSequence;
reserve e, e1, e2 for Singleton of E;

theorem
  for E being finite non empty set, A,B being Event of E holds prob(A \/
  B) <= prob(A) + prob(B)
proof
  let E be finite non empty set, A,B be Event of E;
  prob(A \/ B) = prob(A) + prob(B) - prob(A /\ B) by Th20;
  hence thesis by Th18,XREAL_1:43;
end;
