theorem Th29: :: JORDAN1B:29

for n being Nat
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for i being Nat st 1 <= i & i <= len (Gauge (C,n)) holds
LSeg (((Gauge (C,n)) * (i,1)),((Gauge (C,n)) * (i,(len (Gauge (C,n)))))) meets Upper_Arc (L~ (Cage (C,n)))