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 Th4;
s < q by A1, Th4;
hence s in [.p,q.[ by A2, Th3; :: thesis: verum