Hey there I also need some help on this proof as well.

Imagine an infinite chessboard that contains a positive integer in each square. If the value in each square is equal to the average of its four neighbors to the north, east, south and west prove the values in all the squares are equal.

I understand this problem conceptually, but I can seem to put this in words. I hope someone can guide me through the problem step by step, so I can understand how to do this problem, thanks.