reserve x, y, z, r, s, t for Real;

theorem
  |.x.| <= z & |.y.| <= t implies |.x+y.| <= z + t
proof
  assume |.x.| <= z & |.y.| <= t;
  then |.x+y.| <= |.x.| + |.y.| & |.x.| + |.y.| <= z + t by COMPLEX1:56
,XREAL_1:7;
  hence thesis by XXREAL_0:2;
end;
