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
  -p = - p.1*<e1> - p.2*<e2> - p.3*<e3>
proof
   -p = (-1)*p.1*<e1> + (-1)*p.2*<e2> + (-1)*p.3*<e3> by Th30
     .= -p.1*<e1> + ((-1)*p.2)*<e2> + (-p.3)*<e3> by RVSUM_1:49
     .= -p.1*<e1> + -p.2*<e2> +((-1)*p.3)*<e3> by RVSUM_1:49
     .= - p.1*<e1> - p.2*<e2> - p.3*<e3> by RVSUM_1:49;
   hence thesis;
end;
