Does believing in the Hereafter (Day of Judgement) lead to believing in the Holy Book (Al-Quran) and sincerely following the instructions therein?

Verses 91-92 of Chapter 6:

Those people formed quite a wrong estimate of Allah, when they said, "Allah has not sent down anything to any man." Ask them: "Then who sent down the Book, which Moses brought: which was Light and Guidance for mankind: which you have divided into fragments, a part of which you show to the people and most of it you hide from them: by which you were given that knowledge which neither you nor your forefathers possessed?" -- Just say, "Allah", and then leave them alone to play with their useless arguments. (Like that Book) this is a Book which We have sent down; it is a blessed Book, it confirms that which was sent down before it, and this has been sent down so that you should warn the people of this central place (Makkah) and those who dwell around it. Those, who believe in the Hereafter, believe in this Book, and observe their prescribed Prayers punctually.