theorem
  L is subst-correct implies
  for a being SortSymbol of J st x in X.a & x nin (vf A).a
  holds A\iff\for(x,A) in G
  proof
    assume
A1: L is subst-correct;
    let a be SortSymbol of J; assume
A2: x in X.a & x nin (vf A).a;
A3: \for(x,A\impA)\imp(\for(x,A)\impA) in G by A1,Th107;
    A\impA in G by Th34;
    then \for(x,A\impA) in G by Def39;
    then \for(x,A)\impA in G & A\imp\for(x,A) in G by A2,A3,Def38,Th108;
    hence thesis by Th43;
  end;
