let x, n, k, i be Nat; :: thesis: ( i in Seg n implies DigA (DecSD x,n,k),i >= 0 )
assume A1: i in Seg n ; :: thesis: DigA (DecSD x,n,k),i >= 0
then A2: i >= 1 by FINSEQ_1:3;
DigA (DecSD x,n,k),i = DigitDC x,i,k by A1, RADIX_1:def 9
.= (x mod ((Radix k) |^ i)) div ((Radix k) |^ (i -' 1)) by RADIX_1:def 8
.= (x div ((Radix k) |^ (i -' 1))) mod (Radix k) by A2, RADIX_2:4, RADIX_2:6 ;
hence DigA (DecSD x,n,k),i >= 0 ; :: thesis: verum