let p, q, r, s be ExtReal; ( r <= p & r <= s implies not [.r,s.] c= ].p,q.] )
assume that
A1:
r <= p
and
A2:
r <= s
; not [.r,s.] c= ].p,q.]
take
r
; MEMBERED:def 8 ( r in [.r,s.] & not r in ].p,q.] )
thus
r in [.r,s.]
by A2, Th1; not r in ].p,q.]
thus
not r in ].p,q.]
by A1, Th2; verum