reserve A,B,C for non empty set,
  f for Function of [:A,B:],C;
reserve K for non empty doubleLoopStr;

theorem
  for K being Field holds opp(K) is strict Field
proof
  let K be Field;
  set L = opp(K);
  for x,y being Scalar of L holds x*y = y*x
  proof
    let x,y be Scalar of L;
    reconsider a = x, b = y as Scalar of K;
    b*a = x*y by Lm3;
    hence thesis by Lm3;
  end;
  hence thesis by GROUP_1:def 12;
end;
