
theorem
  for p, q, r, s being Real st p < r & r <= s & s < q holds
    [.r,s.] c< [.p,q.]
proof
 let p, q, r, s be Real;
 assume A1: p < r & r <= s & s < q; then
 r <= q by XXREAL_0:2; then
 A3: p <= q by XXREAL_0:2,A1;
 ex x being object st x in [.p,q.] & not x in [.r,s.]
 proof
  take q;
  thus thesis by XXREAL_1:1,A1,A3;
 end;
 hence thesis by XBOOLE_0:def 8,XXREAL_1:34,A1;
end;
