theorem Th8: :: RADIX_4:8

for n, k, x, y, i being Nat st i in Seg n & 2 <= k holds
SDSubAddDigit ((SD2SDSub (DecSD (x,(n + 1),k))),(SD2SDSub (DecSD (y,(n + 1),k))),i,k) = SDSubAddDigit ((SD2SDSub (DecSD ((x mod ((Radix k) |^ n)),n,k))),(SD2SDSub (DecSD ((y mod ((Radix k) |^ n)),n,k))),i,k)