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, y1, 0]| <X> |[0, y2, 0]| = 0.TOP-REAL 3
proof
  |[0, y1, 0]| <X> |[0, y2, 0]| = |[ (y1 * 0) - (0 * y2), (0 * 0) - (0 * 0
  ), (0 * y2) - (y1 * 0) ]|
    .= |[ 0 * (y1 - y2), 0 * (0 - 0), 0 * (y2 - y1) ]|
    .= 0 * |[ (y1 - y2), (0 - 0), (y2 - y1) ]| by Th8
    .= 0.TOP-REAL 3 by RLVECT_1:10;
  hence thesis;
end;
