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 Th22:
  r*<e2> = |[ 0,r,0 ]|
proof
<e2>.1 = 0 & <e2>.2 = 1 & <e2>.3 = 0;
    then r*<e2> = |[ r*0,r*1,r*0 ]| by Lm1 .= |[ 0,r,0 ]|;
   hence thesis;
end;
