C++ std::set upper_bound iterator behaviour

I had a lookup problem to code and was unsure about correct interpretation of iterator testing. The problem is this: I have a set and do a lookup using upper_bound, then want to find the next lowest element. Like this:

#include <iostream>
#include <set>
#include <algorithm>

void exploreSet(std::set<int> &int_set, int key);

int main()
{
    std::set<int> int_set { 5, 10, 12, 17, 19 };
    exploreSet(int_set, 15);
    exploreSet(int_set, 4);
    return 0;
}


void exploreSet(std::set<int> &int_set, int key)
{
    auto it = int_set.upper_bound(key);
    if ( it==int_set.end() )
    {
        std::cout << "Nothing found.\n";
    }
    else
    {
        std::cout << "Found " << *it << ".\n";
        // Now find the next lowest value -- how?
        auto it_back = it;
        --it_back;
        if ( it_back==int_set.end() )
        {
            std::cout << "Nothing prior.\n";
        }
        else
        {
            std::cout << "Prior value:  " << *it_back << ".\n";
        }
    }
}

Resulting output of running this on gcc 4.9.2 with std=c++14:

Found 17.
Prior value:  12.
Found 5.
Nothing prior.

This works. But why?

Is it correct to compare against std::set::end() when going backwards on an iterator obtained through upper_bound? Why or why not?