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 Th74:
  p1<X>p2 = -p2<X>p1
proof
  -p2<X>p1 = |[ (-1)*((p2.2*p1.3)-(p2.3*p1.2)),(-1)*((p2.3*p1.1)-(p2.1*p1.3)),
       (-1)*((p2.1*p1.2)-(p2.2*p1.1)) ]| by Th50
          .= p1<X>p2;
   hence thesis;
end;
