theorem Th4: :: JORDAN19:4

for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for n being Nat st n > 0 holds
for i, j being Nat st 1 <= i & i <= len (Gauge (C,n)) & 1 <= j & j <= width (Gauge (C,n)) & (Gauge (C,n)) * (i,j) in L~ (Cage (C,n)) holds
LSeg (((Gauge (C,n)) * (i,(width (Gauge (C,n))))),((Gauge (C,n)) * (i,j))) meets Upper_Arc (L~ (Cage (C,n)))