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 Th43:
  mlt(p,q) = <* p.1*q.1, p.2*q.2, p.3*q.3 *>
proof
 len p = 3 & len q = 3 by Th42;
    hence thesis by EUCLID_5:28;
end;
