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, Th2; :: thesis: verum