theorem :: JORDAN1E:21

for n being Nat
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for k being Nat st 1 <= k & k + 1 <= len (Cage (C,n)) & (Cage (C,n)) /. k = S-max (L~ (Cage (C,n))) holds
((Cage (C,n)) /. (k + 1)) `2 = S-bound (L~ (Cage (C,n)))