
theorem
  for S be non empty finite set,
  D be EqSampleSpaces of S,
  f be Function of S,BOOLEAN
  holds Prob(('not' f),D) = 1 - Prob(f,D)
  proof
    let S be non empty finite set,
    D be EqSampleSpaces of S,
    f be Function of S,BOOLEAN;
    set s = the Element of D;
    thus Prob(('not' f),D)= Prob(('not' f),s) by Def6
    .= 1 - Prob(f,s) by Th26
    .= 1 - Prob(f,D) by Def6;
  end;
