theorem Th5: :: JORDAN1D:5

for i, m, n being Nat
for D being compact non horizontal non vertical Subset of (TOP-REAL 2) st 2 <= m & m + 1 < len (Gauge (D,i)) & 2 <= n & n + 1 < len (Gauge (D,i)) holds
cell ((Gauge (D,i)),m,n) = (((cell ((Gauge (D,(i + 1))),((2 * m) -' 2),((2 * n) -' 2))) \/ (cell ((Gauge (D,(i + 1))),((2 * m) -' 1),((2 * n) -' 2)))) \/ (cell ((Gauge (D,(i + 1))),((2 * m) -' 2),((2 * n) -' 1)))) \/ (cell ((Gauge (D,(i + 1))),((2 * m) -' 1),((2 * n) -' 1)))