theorem Th57: :: JORDAN1A:57

for n being Nat
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2) ex k, t being Nat st
( 1 <= k & k < len (Cage (C,n)) & 1 <= t & t <= width (Gauge (C,n)) & (Cage (C,n)) /. k = (Gauge (C,n)) * ((len (Gauge (C,n))),t) )