for i, j, k, m being Nat
for C being compact non horizontal non vertical Subset of (TOP-REAL 2) st m > k & [i,j] in Indices (Gauge (C,k)) & [(i + 1),j] in Indices (Gauge (C,k)) holds
dist (((Gauge (C,m)) * (i,j)),((Gauge (C,m)) * ((i + 1),j))) < dist (((Gauge (C,k)) * (i,j)),((Gauge (C,k)) * ((i + 1),j)))