
theorem Th8:
  for S be non empty finite set,
  f be S-valued Function,
  judgefunc be Function of S,BOOLEAN holds
  trueEVENT(judgefunc*f) is Event of dom f
  proof
    let S be non empty finite set,
    f be S-valued Function,
    judgefunc be Function of S,BOOLEAN;
    for x be object st x in dom (judgefunc*f)
    holds x in dom f by FUNCT_1:11; then
    dom (judgefunc*f) c= dom f by TARSKI:def 3;
    hence thesis by XBOOLE_1:1;
  end;
