theorem Th30:
  for f being FinSequence of CQC-WFF(Al) holds
  still_not-bound_in rng f = still_not-bound_in f
proof
  let f be FinSequence of CQC-WFF(Al);
  set A = {still_not-bound_in p : p in rng f};
A1: now
    let a be object;
    assume a in still_not-bound_in rng f;
    then consider b being set such that
A2: a in b and
A3: b in A by TARSKI:def 4;
    consider p such that
A4: b = still_not-bound_in p and
A5: p in rng f by A3;
    ex c being object st ( c in dom f)&( f.c = p) by A5,FUNCT_1:def 3;
    hence a in still_not-bound_in f by A2,A4,CALCUL_1:def 5;
  end;
  now
    let a be object;
    assume a in still_not-bound_in f;
    then consider i being Nat,q such that
A6: i in dom f and
A7: q = f.i and
A8: a in still_not-bound_in q by CALCUL_1:def 5;
    q in rng f by A6,A7,FUNCT_1:def 3;
    then still_not-bound_in q in A;
    hence a in still_not-bound_in rng f by A8,TARSKI:def 4;
  end;
  hence thesis by A1,TARSKI:2;
end;
