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, Th2; :: thesis: verum