let p, q be ext-real number ; :: thesis: ].p,q.] c= [.p,q.]
let s be ext-real number ; :: 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 Th2;
s <= q by A1, Th2;
hence s in [.p,q.] by A2, Th1; :: thesis: verum