theorem
 |.|[0,a]|.| = |.a.| & |.|[a,0]|.| = |.a.|
proof
  reconsider aa = a as Real;
  reconsider a2 = aa^2, z2 = 0^2 as Real;
  |.<*0,aa*>.| = sqrt Sum <*z2,a2*> by Th10
    .= sqrt (0+a^2) by RVSUM_1:77
    .= |.a.| by COMPLEX1:72;
  hence |.|[0,a]|.| = |.a.|;
  |.<*aa,0 *>.| = sqrt Sum <*a2,z2 *> by Th10
    .= sqrt (a^2+0) by RVSUM_1:77
    .= |.a.| by COMPLEX1:72;
  hence thesis;
end;
