
theorem Th1:
  for k be Nat st k >= 2 holds Radix(k) - 1 in k-SD
proof
  let k be Nat;
  assume k >= 2;
  then Radix(k) > 2 by RADIX_4:1;
  then Radix(k) > 1 by XXREAL_0:2;
  then Radix(k) + Radix(k) > 1 + 1 by XREAL_1:8;
  then
A1: Radix(k) - 1 > 0 + 1 - Radix(k) by XREAL_1:21;
  k-SD = {w where w is Element of INT:w <= Radix(k)-1 & w >= -Radix(k)+1}
  & Radix(k) - 1 is Element of INT by INT_1:def 2,RADIX_1:def 2;
  hence thesis by A1;
end;
