
theorem Th5:
  for i,k,n be Nat st i in Seg n holds DigA(DecSD(0,n,k),i) = 0
proof
  let i,k,n be Nat;
  assume
A1: i in Seg n;
  then
A2: i >= 1 by FINSEQ_1:1;
  DigA(DecSD(0,n,k),i) = DigitDC(0,i,k) by A1,RADIX_1:def 9
    .= (0 mod (Radix(k) |^ i)) div (Radix(k) |^ (i-'1)) by RADIX_1:def 8
    .= (0 div (Radix(k) |^ (i-'1))) mod Radix(k) by A2,RADIX_2:4,6
    .= 0 mod Radix(k);
  hence thesis by NAT_D:26;
end;
