theorem Th35:
  B is quantifiable & B1 is quantifiable & Sub_All(B,SQ) = Sub_All
  (B1,SQ1) implies B`2 = B1`2 & SQ = SQ1
proof
  assume that
A1: B is quantifiable and
A2: B1 is quantifiable & Sub_All(B,SQ) = Sub_All(B1,SQ1);
  Sub_All(B,SQ) = [All(B`2,(B`1)`1),SQ] by A1,SUBSTUT1:def 24;
  then
A3: [All(B`2,(B`1)`1),SQ] = [All(B1`2,(B1`1)`1),SQ1] by A2,SUBSTUT1:def 24;
  then All(B`2,(B`1)`1) = All(B1`2,(B1`1)`1) by XTUPLE_0:1;
  hence thesis by A3,QC_LANG2:5,XTUPLE_0:1;
end;
