
theorem Th5:
  for x,n,k,i be Nat st i in Seg n holds DigA(DecSD(x,n,k),i) >= 0
proof
  let x,n,k,i be Nat;
  assume
A1: i in Seg n;
  then
A2: i >= 1 by FINSEQ_1:1;
  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_2:4,6;
  hence thesis;
end;
