theorem
  L is vf-qc-correct implies
  \for(x,A)\imp\for(x,x,A) in G
  proof assume
A1: L is vf-qc-correct;
    consider a being object such that
A2: a in dom X & x in X.a by CARD_5:2;
    reconsider a as Element of J by A2;
    set Y = X extended_by({}, the carrier of S1);
A3: a is SortSymbol of S1 by Th8;
A4: x nin (vf\for(x,A)).a by A1,A2,A3,Th113;
    \for(x,A)\imp\for(x,A) in G by Th34;
    then \for(x,\for(x,A)\imp\for(x,A)) in G by Def39;
    hence thesis by A2,A4,Th108;
  end;
