theorem Th42:
  0.TOP-REAL 3 <X> p = 0.TOP-REAL 3 & p <X> 0.TOP-REAL 3 = 0.TOP-REAL 3
  proof
A1: 0.TOP-REAL 3 <X> p = |[0,0,0]| <X> |[p`1,p`2,p`3]| by EUCLID_5:3,EUCLID_5:4
                      .= 0.TOP-REAL 3 by EUCLID_5:19;
    p <X> 0.TOP-REAL 3 = - 0.TOP-REAL 3 by A1,EUCLID_5:17
                      .= 0.TOP-REAL 3 by RLVECT_1:12;
    hence thesis by A1;
  end;
