theorem Th24:
  S is Sub_universal implies len@((Sub_the_scope_of(S))`1) < len @ (S`1)
proof
  assume S is Sub_universal;
  then consider B,SQ such that
A1: S = Sub_All(B,SQ) & B is quantifiable;
  S = [All(B`2,(B`1)`1),SQ] by A1,Def24;
  then
A2: S`1 = All(B`2,(B`1)`1);
  All(B`2,(B`1)`1) is universal;
  then
A3: len @the_scope_of All(B`2,(B`1)`1) < len @(S`1) by A2,QC_LANG1:16;
  (Sub_the_scope_of(S))`1 = (B`1)`1 by A1,Th21;
  hence thesis by A3,QC_LANG2:7;
end;
