let n, k be Nat; :: thesis: ( n >= 1 & k >= 2 implies SDDec (DecSD 1,n,k) = 1 )
assume A1:
( n >= 1 & k >= 2 )
; :: thesis: SDDec (DecSD 1,n,k) = 1
then A2:
Radix k > 2
by RADIX_4:1;
Radix k >= 0 + 1
by INT_1:20, RADIX_2:6;
then
(Radix k) |^ n >= Radix k
by A1, PREPOWER:20;
then
(Radix k) |^ n >= 2
by A2, 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_1:25; :: thesis: verum