theorem :: JORDAN1D:22

for n being Nat
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2) ex i being Nat st
( 1 <= i & i <= len (Gauge (C,n)) & N-max (L~ (Cage (C,n))) = (Gauge (C,n)) * (i,(width (Gauge (C,n)))) )