let q, s, r, p be ext-real number ; :: 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, Th1; :: thesis: not t in ].p,q.[
thus not t in ].p,q.[ by A1, Th4; :: thesis: verum