reserve i,n,m,k,x for Nat,
  i1,i2 for Integer;

theorem Th2:
  k-SD_Sub_S c= k-SD_Sub
proof
  let e be object;
  assume e in k-SD_Sub_S;
  then consider g being Element of INT such that
A1: e = g and
A2: g >= -Radix(k-'1) and
A3: g <= Radix(k-'1) - 1;
  Radix(k-'1) + 1 >= Radix(k-'1) + 0 by XREAL_1:7;
  then -Radix(k-'1) >= -(Radix(k-'1) + 1) by XREAL_1:24;
  then
A4: g >= -Radix(k-'1) - 1 by A2,XXREAL_0:2;
  Radix(k-'1) + 0 >= Radix(k-'1) + -1 by XREAL_1:7;
  then Radix(k-'1) >= g by A3,XXREAL_0:2;
  hence thesis by A1,A4;
end;
