reserve
  r,s,r0,s0,t for Real;

theorem Th2:
  |.|.r0-s0.|-|.r-s.|.| <= |.r0-r.| + |.s0-s.|
proof
  r0-s0 - (r-s) = r0-r - (s0-s);
  then
A1: |.r0-s0 - (r-s).| <= |.r0-r.| + |.s0-s.| by COMPLEX1:57;
  |.|.r0-s0.| - |.r-s.|.| <= |.r0-s0 - (r-s).| by COMPLEX1:64;
  hence thesis by A1,XXREAL_0:2;
end;
