theorem
for
p1,
p2,
p3,
p4 being
Point of
(TOP-REAL 2) for
P being non
empty compact Subset of
(TOP-REAL 2) st
P is
being_simple_closed_curve &
p1 in P &
p2 in P &
p3 in P &
p4 in P &
LE p2,
p3,
P &
LE p3,
p4,
P & not
LE p1,
p2,
P & not (
LE p2,
p1,
P &
LE p1,
p3,
P ) & not (
LE p3,
p1,
P &
LE p1,
p4,
P ) holds
LE p4,
p1,
P by Th73;