theorem
  for K being add-associative right_zeroed right_complementable
  Abelian non empty addLoopStr, a1,a2 being Element of K holds
  a1 = -a2 implies -a1 = a2
  proof
    let K be add-associative right_zeroed right_complementable Abelian
    non empty addLoopStr, a1,a2 be Element of K;
    assume a1 = -a2;
    then a1 + a2 = 0.K by VECTSP_1:16;
    hence thesis by VECTSP_1:16;
  end;
