> a case where x+=y was not equivalent to x=x+y

This is true for lists in Python. `a = a + b` creates a new list, but `a += b` works in-place:

    >>> a = [1, 2]
    >>> b = a
    >>> a = a + [3]
    >>> print(a, b)
    [1, 2, 3] [1, 2]

    >>> a = [1, 2]
    >>> b = a
    >>> a += [3]
    >>> print(a, b)
    [1, 2, 3] [1, 2, 3]

There are other issues with the `+=`-style operators as well - IMO it was a mistake to have `a += b` be anything other than a shorthand for `a = a + b`.