theorem Th109:
  ||.x.|| - ||.y.|| <= ||.x - y.||
proof
  (x - y) + y = x - (y - y) by RLVECT_1:29
    .= x - 09(CNS) by RLVECT_1:15
    .= x by RLVECT_1:13;
  then ||.x.|| <= ||.x - y.|| + ||.y.|| by Def13;
  hence thesis by XREAL_1:20;
end;
