theorem Th42:
  ||.-x.|| = ||.x.||
proof
  ||.-x.|| = ||.(-1r) * x.|| by CLVECT_1:3
    .= |.-1r.| * ||.x.|| by Th38
    .= |.1r.| * ||.x.|| by COMPLEX1:52;
  hence thesis by COMPLEX1:48;
end;
