reserve k,m,n for Nat,
  i1,i2,i3 for Integer,
  e for set;
reserve i,k,m,n,p,x,y for Nat;

theorem Th9:
  k-SD c= (k+1)-SD
proof
  let e be object;
  assume e in k-SD;
  then consider g being Element of INT such that
A1: e = g and
A2: g <= Radix(k)-1 and
A3: g >= -Radix(k)+1;
  k < k+1 by NAT_1:13;
  then
A4: 2 to_power k < 2 to_power (k+1) by POWER:39;
  then -Radix(k) > -Radix(k+1) by XREAL_1:24;
  then -Radix(k)+1 > -Radix(k+1)+1 by XREAL_1:6;
  then
A5: g >= -Radix(k+1)+1 by A3,XXREAL_0:2;
  Radix(k)-1 < Radix(k+1)-1 by A4,XREAL_1:9;
  then g <= Radix(k+1)-1 by A2,XXREAL_0:2;
  hence thesis by A1,A5;
end;
