 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
  {g,h}" = {g",h"}
proof
  thus {g,h}" c= {g",h"}
  proof
    let x be object;
    assume x in {g,h}";
    then consider a such that
A1: x = a" and
A2: a in {g,h};
    a = g or a = h by A2,TARSKI:def 2;
    hence thesis by A1,TARSKI:def 2;
  end;
  let x be object;
  assume x in {g",h"};
  then
A3: x = g" or x = h" by TARSKI:def 2;
  g in {g,h} & h in {g,h} by TARSKI:def 2;
  hence thesis by A3;
end;
