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 Th2; :: thesis: verum