reserve a,b,c for positive Real,
  m,x,y,z for Real,
  n for Nat,
  s,s1,s2,s3,s4,s5 for Real_Sequence;

theorem
  |.|.x.|-|.y.|.|<=|.x.|+|.y.|
proof
  |.|.x.|-|.y.|.|<=|.x-y.| & |.x-y.|<=|.x.|+|.y.| by COMPLEX1:57,64;
  hence thesis by XXREAL_0:2;
end;
