theorem Th31:
  [S,x] is quantifiable implies CQCQuant(CQCSub_All([S,x],xSQ),
  CQC_Sub(S)) = All(S_Bound(@CQCSub_All([S,x],xSQ)),CQC_Sub(S))
proof
  set S1 = CQCSub_All([S,x],xSQ);
  set p = CQC_Sub(CQCSub_the_scope_of S1);
A1: Quant(S1,p) = All(S_Bound(@S1),p) by SUBSTUT1:def 37;
  assume
A2: [S,x] is quantifiable;
  then CQCSub_All([S,x],xSQ) = Sub_All([S,x],xSQ) by Def5;
  then CQCSub_All([S,x],xSQ) is Sub_universal by A2,SUBSTUT1:14;
  then
A3: CQCQuant(S1,p) = Quant(S1,p) by Def7;
  CQCQuant(S1,CQC_Sub(S)) = CQCQuant(S1,p) by A2,Th30;
  hence thesis by A2,A3,A1,Th30;
end;
