your proof would read better if you use x~y for xRy instead of "=". you also have a typo in your proof for symmetry, it should read y~x, not y~y.

your listing of the elements of the equivalence classes would be more convincing with the inclusion of negative integers as well:

[0] = {...-8,-4,0,4,8,....}

[1] = ?

etc.

for example, what is [-3]?