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

theorem
  s < p implies [.r,s.] misses [.p,q.[
proof
  assume
A1: s < p;
  let t;
  assume t in [.r,s.];
  then t <= s by Th1;
  then t < p by A1,XXREAL_0:2;
  hence thesis by Th3;
end;
