theorem :: RADIX_2:11

for k, n being Nat st n >= 1 holds
for x, y being Tuple of n,k -SD st k >= 2 holds
(SDDec (x '+' y)) + ((SD_Add_Carry ((DigA (x,n)) + (DigA (y,n)))) * ((Radix k) |^ n)) = (SDDec x) + (SDDec y)