let r, s be ExtReal; :: thesis: [.r,s.[ misses {s}
let t be ExtReal; :: according to MEMBERED:def 20 :: thesis: ( not t in [.r,s.[ or not t in {s} )
assume t in [.r,s.[ ; :: thesis: not t in {s}
then t < s by Th3;
hence not t in {s} by TARSKI:def 1; :: thesis: verum