theorem
  i < j implies len Gauge(D,i) < len Gauge(D,j)
proof
  assume i < j;
  then
A1: 2|^i < 2|^j by PEPIN:66;
  len Gauge(D,i) = 2|^i + 3 & len Gauge(D,j) =2|^j + 3 by JORDAN8:def 1;
  hence thesis by A1,XREAL_1:6;
end;
