theorem :: JORDAN1A:48
for i, j, m, n being Nat
for E being compact non horizontal non vertical Subset of (TOP-REAL 2) st m <= n & 3 <= i & i < len (Gauge (E,m)) & 1 < j & j + 1 < width (Gauge (E,m)) holds
for i1, j1 being Nat st i1 = ((2 |^ (n -' m)) * (i - 2)) + 2 & j1 = ((2 |^ (n -' m)) * (j - 2)) + 2 holds
cell ((Gauge (E,n)),(i1 -' 1),j1) c= cell ((Gauge (E,m)),(i -' 1),j)