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 Th56:
  |.p.| = sqrt ((p.1)^2+(p.2)^2+(p.3)^2)
proof
  |.p.| = sqrt Sum<* p.1*p.1,p.2*p.2,p.3*p.3 *> by Th43
      .= sqrt ((p.1)^2+(p.2)^2+(p.3)^2) by RVSUM_1:78;
  hence thesis;
end;
