theorem Th80: :: JORDAN1A:80

for i, n being Nat
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for p, x being Point of (TOP-REAL 2) st x in S-most C & p in south_halfline x & 1 <= i & i < len (Cage (C,n)) & p in LSeg ((Cage (C,n)),i) holds
LSeg ((Cage (C,n)),i) is horizontal