let p, q be ExtReal; :: thesis: [.p,q.[ c= [.p,q.]
let s be ExtReal; :: according to MEMBERED:def 8 :: thesis: ( not s in [.p,q.[ or s in [.p,q.] )
assume A1: s in [.p,q.[ ; :: thesis: s in [.p,q.]
then A2: p <= s by Th3;
s < q by A1, Th3;
hence s in [.p,q.] by A2, Th1; :: thesis: verum