theorem Th114:
  L is vf-qc-correct implies
  for a being SortSymbol of S1 st x in X.a holds x nin (vf \ex(x,A)).a
  proof
    assume
A1: L is vf-qc-correct;
    let a be SortSymbol of S1; assume x in X.a;
    then vf \ex(x,A) = (vf A)(\)(a-singleton x) by A1;
    then
A2: (vf \ex(x,A)).a = ((vf A).a) \ ((a-singleton x).a) by PBOOLE:def 6
    .= (vf A).a \ {x} by AOFA_A00:6;
    x in {x} by TARSKI:def 1;
    hence thesis by A2,XBOOLE_0:def 5;
  end;
