C++ Segmentation_Fault With Set

I’m relatively new to c++, and trying to understand why my following code is recieving segmentation fault:

#include <iostream>
#include <set>
using namespace std;

set<int> S;

int main(){
    S.insert(1);

    auto it = S.lower_bound(1);
    cout << *it << endl;
    cout << (it-- == S.begin()) << endl;
}

1. Correct me if I’m wrong, but doesn’t c++ allow you to decrement your iterator, as long as your iterator is within S.begin() to S.end(), inclusive?
2. Why does it work to test an iterator for S.begin() for it to be out of bounds? Isn’t the element S.begin() also a valid element inside set S?

>Solution :

From the c++ref

The begin iterator is not decrementable and the behavior is undefined if –container.begin() is evaluated.