Proof of correctness recursive reverse digit function

Question

This is an attempt to understand better recursion. The following recursive function returns the integer obtained by reversing the digits of an input integer. I'm trying to prove its correctness:

public static int reverse(int n)
{
    return reverse(n, 0);
}
public static int reverse(int number, int reverted)
{
    if (number!=0)
        return reverse(number/10, reverted*10 + number % 10); 
    else
        return reverted;
}

The program requires the integer input to be strictly positive, and the program clearly terminates because n is decreasing. Moreover, we have the relation

reverse(xy, z) = z*reverse(xy) = z*reverse(y)*reverse(x)

How should I proceed to complete a formal proof of correctness for recursion?