reserve C for Simple_closed_curve,
  i for Nat;
reserve R for non empty Subset of TOP-REAL 2,
  j, k, m, n for Nat;

theorem Th11:
  for C being non vertical non horizontal compact Subset of
TOP-REAL 2 holds m > k implies dist(Gauge(C,m)*(1,1),Gauge(C,m)*(2,1)) < dist(
  Gauge(C,k)*(1,1),Gauge(C,k)*(2,1))
proof
  let C be non vertical non horizontal compact Subset of TOP-REAL 2;
  assume
A1: m > k;
  [1+1,1] in Indices Gauge(C,k) by Th7;
  hence thesis by A1,Th5,Th10;
end;
