reserve a,b,c,d,e,f for Real,
        k,m for Nat,
        D for non empty set,
        V for non trivial RealLinearSpace,
        u,v,w for Element of V,
        p,q,r for Element of ProjectiveSpace(V);
reserve o,p,q,r,s,t for Point of TOP-REAL 3,
        M for Matrix of 3,F_Real;

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;
