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 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 t in ].p,q.[ by A6, Th4; :: thesis: verum