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 s in [.p,q.[ ; :: thesis: s in [.p,q.]
then ( p <= s & s < q ) by Th3;
hence s in [.p,q.] by Th1; :: thesis: verum