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 Th3;
then t < p by A1, XXREAL_0:2;
hence not t in [.p,q.[ by Th3; :: thesis: verum