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 Th3;
A5: t < s by A3, Th3;
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