let p, s, q be ext-real number ; :: thesis: ( p <= s & p < q implies [.p,q.[ \ ].p,s.] = {p} \/ ].s,q.[ )
[.p,p.] = {p} by Th17;
hence ( p <= s & p < q implies [.p,q.[ \ ].p,s.] = {p} \/ ].s,q.[ ) by Th306; :: thesis: verum