theorem Th27:
  |{ p, a * q, r }| = a * |{ p, q, r }|
  proof
    |{p, a * q , r }| = - |{ a *q, p,r}| by Th25
                     .= - (a * |{q,p,r}|) by Th26
                     .= - (a * (- |{p,q,r}|)) by Th25;
    hence thesis;
  end;
