let r, s be ExtReal; ( r <= s implies [.r,s.] \ {r,s} = ].r,s.[ )
assume
r <= s
; [.r,s.] \ {r,s} = ].r,s.[
then A1:
[.r,s.] = ].r,s.[ \/ {r,s}
by Th128;
A2:
not r in ].r,s.[
by Th4;
not s in ].r,s.[
by Th4;
hence
[.r,s.] \ {r,s} = ].r,s.[
by A1, A2, ZFMISC_1:121; verum