let p, q, r, s be ExtReal; :: thesis: ( p <= r & s < q implies [.r,s.] c= [.p,q.[ )
assume that
A1: p <= r and
A2: s < q ; :: thesis: [.r,s.] c= [.p,q.[
let t be ExtReal; :: according to MEMBERED:def 8 :: thesis: ( not t in [.r,s.] or t in [.p,q.[ )
assume A3: t in [.r,s.] ; :: thesis: t in [.p,q.[
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 t in [.p,q.[ by A6, Th3; :: thesis: verum