reserve x,y,z for Real,
  x3,y3 for Real,
  p for Point of TOP-REAL 3;
reserve p1,p2,p3,p4 for Point of TOP-REAL 3,
  x1,x2,y1,y2,z1,z2 for Real;

theorem
  |[0, 0, z1]| <X> |[0, 0, z2]| = 0.TOP-REAL 3
proof
  |[0, 0, z1]| <X> |[0, 0, z2]| = |[ (0 * z2) - (z1 * 0), (z1 * 0) - (0 *
  z2), (0 * 0) - (0 * 0) ]|
    .= |[ 0 * (z2 - z1), 0 * (z1 - z2), 0 * (0 * 0) ]|
    .= 0 * |[ (z2 - z1), (z1 - z2), (0 - 0) ]| by Th8
    .= 0.TOP-REAL 3 by RLVECT_1:10;
  hence thesis;
end;
