let n, k be Nat; ( n >= 1 & k >= 2 implies SDDec (DecSD (1,n,k)) = 1 )
assume that
A1:
n >= 1
and
A2:
k >= 2
; SDDec (DecSD (1,n,k)) = 1
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
SDDec (DecSD (1,n,k)) = 1
by A1, RADIX_1:22; verum