let p, q, r, s be ExtReal; :: thesis: ( q <= s & r < s implies not ].r,s.] c= ].p,q.[ )
assume that
A1: q <= s and
A2: r < s ; :: thesis: not ].r,s.] c= ].p,q.[
take t = s; :: according to MEMBERED:def 8 :: thesis: ( t in ].r,s.] & not t in ].p,q.[ )
thus t in ].r,s.] by A2, Th2; :: thesis: not t in ].p,q.[
thus not t in ].p,q.[ by A1, Th4; :: thesis: verum