let p, q, r, s be ExtReal; ( r <= s & [.r,s.] c= [.p,q.] implies ( p <= r & s <= q ) )
assume A1:
r <= s
; ( not [.r,s.] c= [.p,q.] or ( p <= r & s <= q ) )
then A2:
r in [.r,s.]
by Th1;
s in [.r,s.]
by A1, Th1;
hence
( not [.r,s.] c= [.p,q.] or ( p <= r & s <= q ) )
by A2, Th1; verum