Intention doesn't transfer to inevitable consequences

Some people, maybe as part of a response to the closeness problem for Double Effect, think:

1. Whenever I intend A while knowing that A inevitably causes B, I intend B.

This is false. Suppose I play a game late at night in order to have late night fun, knowing that late night fun will inevitably lead to my being tired in the morning. Now, if I intend something, I intend it as a means or as an end. I clearly don’t intend to be tired in the morning as a means to having had fun in the evening: there is no backwards causation. But I also don’t intend being tired in the morning as an end: the end was my late night fun, which led to being tired. So if I don’t intend it as a means or as an end, I don’t intend it at all, contrary to 1.

More precisely:

2. I intend E as my end and know that E inevitably causes F.

3. If I intend something, I intend it as a means or as an end.

4. If I know that something is caused by my end, then I do not intend it as an end.

5. If I know that something is caused by my end, then I do not intend it as a means.

6. So, I do not intend F as an end or as a means. (2, 4, 5)

7. So, I do not intend F. (3, 6)

8. So, sometimes I act intending E and knowing that E inevitably causes some effect F without intending F. (2, 7)

9. So, (1) is false.