Note also that the opposite of a hasty generalization is a sweeping generalization. My neighbors on both side of me have won the lottery, so we should play the lottery. Simply because one event precedes another event in time deos not mean that the first event is the cause of the second event. This argument resembles the fallacy known as Hasty Generalization. The argument assumes its conclusion is true but DOES NOT SHOW it to be true.
P is true, because A is true.
And A is true because B is true. And B is true because P is true. Also called circular reasoning. Hidden within the question is another question. This is also called Fallacy of Interrogation.