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
  0 * p = |[ 0,0,0 ]|
proof
  thus 0 * p = |[ 0 * p.1,0 * p.2,0 * p.3]| by Lm1
 .= |[ 0,0,0 ]|;
