theorem Th10:
  ||.x - z.|| <= ||.x - y.|| + ||.y - z.||
proof
  x - z = x + (09(RNS) + (-z))
    .= x + (((-y) + y) + (-z)) by RLVECT_1:5
    .= x + ((-y) + (y + (-z))) by RLVECT_1:def 3
    .= (x - y) + (y - z) by RLVECT_1:def 3;
  hence thesis by Def1;
end;
