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) +
  prob(A` /\ B) = prob(B) + prob(B` /\ A)
proof
  let E be finite non empty set, A,B be Event of E;
  prob(A) = prob(A /\ B) + prob(A /\ B`) & prob(B) = prob(A /\ B) + prob(B
  /\ A`) by Th26;
  hence thesis;
end;
