
theorem Th24:
  for S be non empty finite set,
  D be EqSampleSpaces of S,
  s be Element of D,
  f,g be Function of S,BOOLEAN
  holds Prob((f 'or' g),s) =
  card (trueEVENT(f*s) \/ trueEVENT(g*s))/(len s)
  proof
    let S be non empty finite set,
    D be EqSampleSpaces of S,
    s be Element of D,
    f,g be Function of S,BOOLEAN;
    A1: s is Element of S* by FINSEQ_1:def 11;
    trueEVENT((f 'or' g)*s)=Coim((f 'or' g)*s,TRUE)
    .= Coim (f*s,TRUE) \/ Coim (g*s,TRUE) by Th21,A1
    .= trueEVENT(f*s) \/ trueEVENT(g*s);
    hence thesis;
  end;
