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The expression haraj (lit., "straitness" or "tightness") is often used idiomatically to denote "doubt": and this is, according to Ibn 'Abbas, Mujahid and Qatadah, the meaning of the term here (see Tabari, Zamakhshari, Baghawi, Razi, Ibn Kathir). The construction of the whole sentence makes it clear that the "doubt" does not relate to the origin of the divine writ but to its purpose: and thus, although ostensibly addressed to the Prophet, the above passage is meant to draw the attention of all whom the Qur'anic message may reach to the fact that it has a twofold objective - namely, to warn the rejectors of the truth and to guide those who already believe in it. Both the warning and the admonition are summarized in the sequence.
Heart: in the original, breast. I have used the word most appropriate to the English idiom. The meaning is that Al-Mustafa is consoled for all the difficulties which he encountered in his mission, with the fact that he had clear guidance in the Book for his preaching.