theorem Th51:
  [S,x] is quantifiable & x in rng RestrictSub(x,All(x,S`1),xSQ)
implies S_Bound(@CQCSub_All([S,x],xSQ)) = x.upVar(RestrictSub(x,All(x,S`1),xSQ)
  ,S`1)
proof
  set S1 = CQCSub_All([S,x],xSQ);
  assume that
A1: [S,x] is quantifiable and
A2: x in rng RestrictSub(x,All(x,S`1),xSQ);
A3: S1 = Sub_All([S,x],xSQ) by A1,Def5;
  then
A4: S1`2 = xSQ by A1,Th26;
A5: S1`1 = All([S,x]`2,([S,x]`1)`1) by A1,A3,Th26;
  then
A6: S1`1 = All(x,([S,x]`1)`1);
  then
A7: S1`1 = All(x,S`1) & x = bound_in S1`1 by QC_LANG2:7;
  set finSub = RestrictSub(bound_in S1`1,S1`1,S1`2);
A8: @S1 = S1 by SUBSTUT1:def 35;
  S1`1 = All(x,([S,x]`1)`1) by A5;
  then bound_in(S1`1) = x by QC_LANG2:7;
  then bound_in(S1`1) in rng finSub by A2,A4,A6;
  then S_Bound(@S1) = x.upVar(finSub,the_scope_of S1`1) by A8,SUBSTUT1:def 36;
  hence thesis by A4,A7,QC_LANG2:7;
end;
