theorem Th57: :: JORDAN1J:57

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