theorem :: JORDAN1G:36

for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for n, i being Nat st 1 <= i & i <= len (Gauge (C,n)) & n > 0 holds
((Gauge (C,n)) * (i,(Center (Gauge (C,n))))) `2 = ((S-bound C) + (N-bound C)) / 2