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 Th4;
hence s in [.p,q.[ by Th3; :: thesis: verum