The following holds:If from any integer we subtract the sum of its digits, then the result is divisible by 9.E.g. take 1456. The sum of its digits is:

1 + 4 + 5 + 6 = 16. Then: 1456 - 16 = 1440 = 160 x 9.

Give a rigorous proof of the above statement! How does it generalize?