 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))" = {}
proof
  thus ({}(the carrier of G))" c= {}
  proof
    let x be object;
    assume x in ({}(the carrier of G))";
    then ex a st x = a" & a in {}the carrier of G;
    hence thesis;
  end;
  thus thesis;
end;
