theorem
  r1*p-r2*p = (r1-r2)*|[ p.1, p.2, p.3 ]|
proof
  r1*R - r2*R = (r1-r2)*R
  proof
    r1*R - r2*R = r1*R + ((-1)*r2)*R by RVSUM_1:49
     .= (r1 + -r2)*R by RVSUM_1:50;
    hence thesis;
  end; then
  r1*p-r2*p = (r1-r2)*p;
  hence thesis by Th1;
end;
