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

theorem Th43:
  p <= r & s < q implies [.r,s.] c= [.p,q.[
proof
  assume that
A1: p <= r and
A2: s < q;
  let t;
  assume
A3: t in [.r,s.];
  then
A4: r <= t by Th1;
A5: t <= s by A3,Th1;
A6: p <= t by A1,A4,XXREAL_0:2;
  t < q by A2,A5,XXREAL_0:2;
  hence thesis by A6,Th3;
end;
