let n, m, k, i be Nat; :: thesis: ( i in Seg n implies DigA (DecSD m,(n + 1),k),i = DigA (DecSD m,n,k),i )
assume A1: i in Seg n ; :: thesis: DigA (DecSD m,(n + 1),k),i = DigA (DecSD m,n,k),i
then i <= n by FINSEQ_1:3;
then A2: i <= n + 1 by NAT_1:12;
1 <= i by A1, FINSEQ_1:3;
then A3: i in Seg (n + 1) by A2, FINSEQ_1:3;
DigA (DecSD m,n,k),i = DigitDC m,i,k by A1, RADIX_1:def 9
.= DigA (DecSD m,(n + 1),k),i by A3, RADIX_1:def 9 ;
hence DigA (DecSD m,(n + 1),k),i = DigA (DecSD m,n,k),i ; :: thesis: verum