 reserve x for object;
 reserve G for non empty 1-sorted;
 reserve A for Subset of G;
 reserve y,y1,y2,Y,Z for set;
 reserve k for Nat;
 reserve G for Group;
 reserve a,g,h for Element of G;
 reserve A for Subset of G;

theorem
  ([#](the carrier of G))" = the carrier of G
proof
  thus ([#](the carrier of G))" c= the carrier of G;
  let x be object;
  assume x in the carrier of G;
  then reconsider a = x as Element of G;
  a"" in ([#](the carrier of G))";
  hence thesis;
end;
