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 Th3;
  then
A2: min(r,p) <= t by XXREAL_0:23;
  t < max(s,q) by A1,XXREAL_0:30;
  hence thesis by A2,Th3;
end;
