Re: "it1++ is equivalent to it1=it1+1” -- that's not the case. It's true for built-in numeric types, but once overloaded operators come into play, there's no inherent connection between the two operators. Iterators for std::list are forward iterators; they do not have an operator+, but they do have an operator++.
Edit, elaboration:
A forward iterator let’s you move forward in a sequence. To do that, it provides two overloads of operator++, so that you can write it++ and ++it. std::forward_list provides forward iterators.
A bidirectional iterator let’s you move forward and backward in a sequence. In addition to the operations provided by forward iterators, it provides two overloads of operator--, so that you can write it-- and --it. std::list provides bidirectional iterators.
A random access iterator let’s you move to arbitrary places in the sequence. In addition to this operations provided by bidirectional iterators, it provides an overload of operator+ so that you can write it + 3. It also provides an overload of operator[] so that it[n] is equivalent to *(it + n). std::vector provides random access iterators.