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
  p1-p2 = |[ p1.1-p2.1, p1.2-p2.2, p1.3-p2.3 ]|
proof
A1:  (-p2).1 = -p2.1 by Th52;
A2:  (-p2).2 = -p2.2 by Th52;
  (-p2).3 = -p2.3 by Th52;
     then p1+-p2 = |[ p1.1+-p2.1, p1.2+-p2.2, p1.3+-p2.3 ]| by A1,A2,Lm2;
     hence thesis;
end;
