reserve X,Y,Z for set,
        x,y,z for object,
        A,B,C for Ordinal;
reserve U for Grothendieck;

theorem
  GrothendieckUniverse X is Universe &
    for U be Universe st X in U holds GrothendieckUniverse X c= U
proof
   set G=GrothendieckUniverse X;
   thus G is Universe by Def4;
   let U be Universe; assume X in U;
   then U is Grothendieck of X by Def4;
   hence thesis by GDef;
end;
