let f be constant standard special_circular_sequence; LSeg ((NW-corner (L~ f)),(N-min (L~ f))) misses LSeg ((N-max (L~ f)),(NE-corner (L~ f)))
A1:
(N-min (L~ f)) `2 = (N-max (L~ f)) `2
by PSCOMP_1:37;
assume
LSeg ((NW-corner (L~ f)),(N-min (L~ f))) meets LSeg ((N-max (L~ f)),(NE-corner (L~ f)))
; contradiction
then consider p being object such that
A2:
p in LSeg ((NW-corner (L~ f)),(N-min (L~ f)))
and
A3:
p in LSeg ((N-max (L~ f)),(NE-corner (L~ f)))
by XBOOLE_0:3;
reconsider p = p as Point of (TOP-REAL 2) by A2;
(N-max (L~ f)) `1 <= (NE-corner (L~ f)) `1
by PSCOMP_1:38;
then A4:
(N-max (L~ f)) `1 <= p `1
by A3, TOPREAL1:3;
(NW-corner (L~ f)) `1 <= (N-min (L~ f)) `1
by PSCOMP_1:38;
then
p `1 <= (N-min (L~ f)) `1
by A2, TOPREAL1:3;
then A5:
(N-min (L~ f)) `1 >= (N-max (L~ f)) `1
by A4, XXREAL_0:2;
(N-min (L~ f)) `1 <= (N-max (L~ f)) `1
by PSCOMP_1:38;
then
(N-min (L~ f)) `1 = (N-max (L~ f)) `1
by A5, XXREAL_0:1;
hence
contradiction
by A1, Th52, TOPREAL3:6; verum