let p, q, r, s be ExtReal; ( p <= r & s <= q implies ].r,s.[ c= ].p,q.] )
assume that
A1:
p <= r
and
A2:
s <= q
; ].r,s.[ c= ].p,q.]
let t be ExtReal; MEMBERED:def 8 ( not t in ].r,s.[ or t in ].p,q.] )
assume A3:
t in ].r,s.[
; t in ].p,q.]
then A4:
r < t
by Th4;
A5:
t < s
by A3, Th4;
A6:
p < t
by A1, A4, XXREAL_0:2;
t < q
by A2, A5, XXREAL_0:2;
hence
t in ].p,q.]
by A6, Th2; verum