theorem Th49:
  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 Th2;
A5: t <= s by A3,Th2;
A6: p < t by A1,A4,XXREAL_0:2;
  t < q by A2,A5,XXREAL_0:2;
  hence thesis by A6,Th4;
end;
