
theorem Th18:
  for S be non empty finite set,
  s be Element of S*,
  judgefunc be Function of S,BOOLEAN holds
  Coim(judgefunc*s,TRUE) in bool (dom s)
  proof
    let S be non empty finite set,
    s be Element of S*,
    judgefunc be Function of S,BOOLEAN;
    reconsider s0=s as FinSequence of S;
    rng s0 c= S;
    then rng s0 c= dom judgefunc by FUNCT_2:def 1;
    then A1: dom (judgefunc*s0) = dom s0 by RELAT_1:27;
    for x be object st x in Coim(judgefunc*s,TRUE) holds
    x in dom s by A1,FUNCT_1:def 7;
    then
    Coim(judgefunc*s,TRUE) c= dom s by TARSKI:def 3;
    hence thesis;
  end;
