reserve k for Nat;

theorem Th13:
  for n,k be Nat, x be Tuple of n,NAT, y be Tuple of n,k-SD st x = y
  holds SDDec2(x,k) = SDDec(y)
proof
  let n,k be Nat;
  let x be Tuple of n,NAT;
  let y be Tuple of n,k-SD;
  assume x = y;
  then SDDec2(x,k) = Sum DigitSD(y) by Th12;
  hence thesis by RADIX_1:def 7;
end;
