Well, killing Greene was an obvious move by the Corleones that Barzini probably anticipated. Besides, the Corleones were co-owners, so getting rid of a partner isn't such a drastic move in the underworld. In any case, it wouldn't change Barzini's perception of Michael as a mediocre successor and his plans to usurp the Corleones pre-eminent position.
"Generosity. That was my first mistake." "Experience must be our only guide; reason may mislead us." "Instagram is Twitter for people who can't read."
