I need to go through a set and remove elements that meet a predefined criteria.

This is the test code I wrote:

#include <set>
#include <algorithm>

void printElement(int value) {
    std::cout << value << " ";
}

int main() {
    int initNum[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
    std::set<int> numbers(initNum, initNum + 10);
    // print '0 1 2 3 4 5 6 7 8 9'
    std::for_each(numbers.begin(), numbers.end(), printElement);

    std::set<int>::iterator it = numbers.begin();

    // iterate through the set and erase all even numbers
    for (; it != numbers.end(); ++it) {
        int n = *it;
        if (n % 2 == 0) {
            // wouldn't invalidate the iterator?
            numbers.erase(it);
        }
    }

    // print '1 3 5 7 9'
    std::for_each(numbers.begin(), numbers.end(), printElement);

    return 0;
}

At first, I thought that erasing an element from the set while iterating through it would invalidate the iterator, and the increment at the for loop would have undefined behavior. Even though, I executed this test code and all went well, and I can't explain why.

My question: Is this the defined behavior for std sets or is this implementation specific? I am using gcc 4.3.3 on ubuntu 10.04 (32-bit version), by the way.

Thanks!