reserve F for Field,
  x for Element of F,
  V for VectSp of F,
  v for Element of V;

theorem
  for G being add-associative right_zeroed right_complementable non
  empty addLoopStr, v,w being Element of G holds -(-v+w) = -w+v
proof
  let G be add-associative right_zeroed right_complementable non empty
  addLoopStr, v,w be Element of G;
  thus -(-v+w) = -w + --v by RLVECT_1:31
    .= -w + v by RLVECT_1:17;
end;
