let p, q, r, s be ExtReal; :: thesis: ( s < p implies [.r,s.] misses [.p,q.] )
assume A1: s < p ; :: thesis: [.r,s.] misses [.p,q.]
let t be ExtReal; :: according to MEMBERED:def 20 :: thesis: ( not t in [.r,s.] or not t in [.p,q.] )
assume t in [.r,s.] ; :: thesis: not t in [.p,q.]
then t <= s by Th1;
then t < p by A1, XXREAL_0:2;
hence not t in [.p,q.] by Th1; :: thesis: verum