reserve X,Y for set;
reserve G for Group;
reserve n for Nat;

theorem Th4:
  permutations {} = {{}}
  proof
    set P = permutations {};
    thus P c= {{}}
    proof
      let x be object;
      assume x in P;
      then x is Permutation of {} by Th1;
      hence thesis by TARSKI:def 1;
    end;
    let x be object;
    assume x in {{}};
    then x = {}({},{}) by TARSKI:def 1;
    hence thesis;
  end;
