It's a matter of checking the different cases.
The number of zeroes is either 0,1,2,3, or 4.
Suppose there are 0 zeroes, then your list is (0,x,x,x).
But this list already contains a zero so that is a contradiction.
Suppose there are 4 zeroes, then your list is (4,0,0,0).
But 4 zeroes don't even fit, since the first number (n0) is 4.
And so on...
Can you do a couple of cases?