The use of the Death Note in the human world sometimes affects other humans' lives or shortens their original life span, even though their names are not actually written in the Death Note itself. In these cases, no matter the cause, the god of death sees only the original lifespan and not the shortened lifespan.
We saw, that Misas lifespan was shortened because Light was killed by Ryuk. So this means, that you can shorten a persons lifespan with the death note. So let's say, A has a death note and knows that C wants to kill B with a death note. He writes B's name in his death note, thus preventing him from being killed by a death note. So C, can't kill B with a death note anymore. But since the death note can shorten the lifespan of those, whos name isn't written in the death note, C decides to use Y, to set up a trap. C writes:
Y, Car accident. Dies at 12:30, after he produces a deadly poison, which he injects into the food the person he knows as ''B'' eats. After he did this, he will die 9 days later in a car accident.
So, could C shorten B's lifespan in this way, so that he is able to indirectly kill him?