
theorem
  for S be non empty finite set,
  D be EqSampleSpaces of S,
  s be Element of D,
  judgefunc be Function of S,BOOLEAN,
  F be non empty finite set,E be Event of F
  st F = dom s & E = trueEVENT(judgefunc*s) holds
  Prob(judgefunc,s) = prob(E)
  proof
    let S be non empty finite set,
    D be EqSampleSpaces of S,
    s be Element of D,
    judgefunc be Function of S,BOOLEAN,
    F be non empty finite set,
    E be Event of F;
    assume A1:F= dom s & E = trueEVENT(judgefunc*s);
    then card F = card Seg len s by FINSEQ_1:def 3
    .= len s by FINSEQ_1:57;
    hence thesis by A1;
  end;
