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 Th22:
  for E being finite non empty set, A being Event of E holds prob(
  A) = 1 - prob(A`) & prob(A`) = 1 - prob(A)
proof
  let E be finite non empty set, A be Event of E;
  A misses A` by SUBSET_1:24;
  then prob(A \/ A`) = prob(A) + prob(A`) by Th21;
  then prob( [#] E ) = prob(A) + prob(A`) by SUBSET_1:10;
  then 1 = prob(A) + prob(A`) by XCMPLX_1:60;
  hence thesis;
end;
