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