reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem
  ].r,s.] \/ ].p,q.] c= ].min(r,p),max(s,q).]
proof
  let t;
  assume t in ].r,s.] \/ ].p,q.];
  then t in ].r,s.] or t in ].p,q.] by XBOOLE_0:def 3;
  then
A1: r < t & t <= s or p < t & t <= q by Th2;
  then
A2: min(r,p) < t by XXREAL_0:22;
  t <= max(s,q) by A1,XXREAL_0:31;
  hence thesis by A2,Th2;
end;
