theorem
  dist(x - z,y - z) <= dist(z,x) + dist(z,y)
proof
  dist(x - z,y - z) = ||.(x - z) + (z - y).|| by RLVECT_1:33
    .= ||.-(z - x) + (z - y).|| by RLVECT_1:33;
  then dist(x - z,y - z) <= ||.-(z - x).|| + ||.z - y.|| by Th30;
  hence thesis by Th31;
end;
