reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem
  Bags {} = {{}}
proof
  now
    let x be set;
    hereby
      assume x in {{}};
      then x = {} by TARSKI:def 1;
      hence x is bag of {} by PARTFUN1:def 2,RELAT_1:38,def 18;
    end;
    assume x is bag of {};
    then reconsider x9 = x as ManySortedSet of {};
    x9 = {};
    hence x in {{}} by TARSKI:def 1;
  end;
  hence thesis by Def12;
end;
