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

theorem Th5:
  for K being Skew-Field holds opp(K) is Skew-Field
proof
  let K be Skew-Field;
  set L = opp(K);
  for x being Scalar of L holds (x <> 0.L implies ex y be Scalar of L st y
  *x = 1_L) & 0.L <> 1_L
  proof
    let x be Scalar of L;
    x <> 0.L implies ex y be Scalar of L st y*x = 1_L
    proof
      reconsider a = x as Scalar of K;
      assume x <> 0.L;
      then consider b being Scalar of K such that
A1:   a*b = 1_K by VECTSP_2:6;
      reconsider y = b as Scalar of opp(K);
      take y;
      thus thesis by A1,Lm3;
    end;
    hence thesis;
  end;
  hence thesis by STRUCT_0:def 8,VECTSP_1:def 9;
end;
