reserve r, r1, r2, x, y, z,
        x1, x2, x3, y1, y2, y3 for Real;
reserve R, R1, R2, R3 for Element of 3-tuples_on REAL;
reserve p, q, p1, p2, p3, q1, q2 for Element of REAL 3;
reserve f1, f2, f3, g1, g2, g3, h1, h2, h3 for PartFunc of REAL,REAL;
reserve t, t0, t1, t2 for Real;

theorem
  |[ x1,x2,x3 ]| <X> |[ y1,y2,y3 ]|
  = |[ (x2*y3)-(x3*y2),(x3*y1)-(x1*y3),(x1*y2)-(x2*y1) ]|
proof
    set p1 = |[ x1,x2,x3 ]|;
    set p2 = |[ y1,y2,y3 ]|;
    thus thesis;
end;
