theorem :: JORDAN1A:45

for j, m, n being Nat
for E being compact non horizontal non vertical Subset of (TOP-REAL 2) st 1 <= m & m <= n & 1 <= j & j <= width (Gauge (E,n)) holds
LSeg (((Gauge (E,n)) * ((Center (Gauge (E,n))),1)),((Gauge (E,n)) * ((Center (Gauge (E,n))),j))) c= LSeg (((Gauge (E,m)) * ((Center (Gauge (E,m))),1)),((Gauge (E,n)) * ((Center (Gauge (E,n))),j)))