reserve k,m,n for Nat,
  i1,i2,i3 for Integer,
  e for set;
reserve i,k,m,n,p,x,y for Nat;
reserve a for Tuple of n,(k-SD);

theorem Th23:
  m is_represented_by (n+1),k implies DigA(DecSD(m,(n+1),k),n+1) =
  m div (Radix(k) |^ n)
proof
  assume m is_represented_by (n+1),k;
  then
A1: m < Radix(k) |^ (n+1);
  n+1 in Seg (n+1) by FINSEQ_1:3;
  then DigA(DecSD(m,(n+1),k),n+1) = DigitDC(m,n+1,k) by Def9
    .= m div (Radix(k) |^ ((n+1) -'1)) by A1,NAT_D:24
    .= m div (Radix(k) |^ n) by NAT_D:34;
  hence thesis;
end;
