
theorem Th30:
  for S be non empty finite set,
  D be EqSampleSpaces of S,
  f be Function of S,BOOLEAN
  holds 0<= 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;
    Prob(f,D) = Prob(f,s) by Def6
    .= card (trueEVENT(f*s))/(len s);
    hence 0 <= Prob(f,D);
  end;
