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;
