
theorem
  for n,k be Nat st n >= 1 & k >= 2 holds SDDec(DecSD(1,n,k)) = 1
proof
  let n,k be Nat;
  assume that
A1: n >= 1 and
A2: k >= 2;
A3: Radix(k) > 2 by A2,RADIX_4:1;
  Radix(k) >= 0 + 1 by INT_1:7,RADIX_2:6;
  then Radix(k) |^ n >= Radix(k) by A1,PREPOWER:12;
  then Radix(k) |^ n >= 2 by A3,XXREAL_0:2;
  then Radix(k) |^ n > 1 by XXREAL_0:2;
  then 1 is_represented_by n,k by RADIX_1:def 12;
  hence thesis by A1,RADIX_1:22;
end;
