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
  |[x1, 0, 0]| <X> |[x2, 0, 0]| = 0.TOP-REAL 3
proof
  |[x1, 0, 0]| <X> |[x2, 0, 0]| = |[ (0 * 0) - (0 * 0) , (0 * x2) - (x1 *
  0) , (x1 * 0) - (0 * x2) ]|
    .= |[ 0 * (0 - 0), 0 * (x2 - x1), 0 * (x1 - x2) ]|
    .= 0 * |[ (0 - 0), (x2 - x1), (x1 - x2) ]| by Th8
    .= 0.TOP-REAL 3 by RLVECT_1:10;
  hence thesis;
end;
