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 Th5:
  [1,1] in Indices Gauge(R,n)
proof
A1: len Gauge(R,n) = width Gauge(R,n) by JORDAN8:def 1;
  1 <= len Gauge(R,n) by Lm3;
  hence thesis by A1,MATRIX_0:30;
end;
