theorem Th39:
  [S,x] is quantifiable & not x in rng RestrictSub(x,All(x,S`1),
xSQ) implies not S_Bound(@CQCSub_All([S,x],xSQ)) in rng RestrictSub(x,All(x,S`1
  ),xSQ)
proof
  set S1 = CQCSub_All([S,x],xSQ);
  assume that
A1: [S,x] is quantifiable and
A2: not x in rng RestrictSub(x,All(x,S`1),xSQ);
A3: S1 = Sub_All([S,x],xSQ) by A1,Def5;
  then
A4: S1`1 = All([S,x]`2,([S,x]`1)`1) by A1,Th26;
  then
A5: S1`1 = All(x,([S,x]`1)`1);
  set finSub = RestrictSub(bound_in S1`1,S1`1,S1`2);
A6: S1 = @S1 by SUBSTUT1:def 35;
  S1`1 = All(x,([S,x]`1)`1) by A4;
  then
A7: bound_in(S1`1) = x by QC_LANG2:7;
  S1`2 = xSQ by A1,A3,Th26;
  then not bound_in(S1`1) in rng finSub by A2,A7,A5;
  hence thesis by A2,A7,A6,SUBSTUT1:def 36;
end;
