First, I would like to quote the following statements made by Buddhaghosa in Section 57, Anangana Suttavannanaa, Mulapannaasa, Majjimanikaaya Atthakathaa.
Tattha bhagavaa ye sammutivasena desanam sutvaa attham pativijjhitvaa moham pahaaya visesam adhigantum samatthaa tesam sammutidesanam deseti. Ye pana para matthavasena desanam sutvaa attham pativijjhitvaa moham pahaaya visesamadhigantum samatthaa, tesam paramattha- desanam deseti."
"The Buddha Bhagavaa's way of teaching is twofold in terms of the conventional way of teaching (sammutidesanaa) and the ultimate way of teaching (paramatthadesanaa). There, such way of teaching as person, sentient being, woman, man, Royals, Brahmin, gods, and maaro is the conventional way of teaching. Such way of teaching as impermanence, misery, selflessness, aggregates, elements, venues, and Establishment of Recollection (Satipatthaana) is the ultimate way of teaching.
There, the Buddha Bhagavaa delivers the conventional way of teaching to those who are capable of gaining unique insight by hearing the teaching in conventional terms, penetrating the meaning, and removing ignorance. On the other hand, the Buddha delivers the ultimate way of teaching to those who are capable of gaining unique insight by hearing the teachings in ultimate terms, penetrating the meaning, and removing ignorance."
Buddhaghosa also made the following statement in Atthasaalinii, page
223, in Roman edition.
"Abhidhamma is the ultimate way of teaching."
Thus, whenever we find in a Suttam the teachings of impermanence, misery, selflessness, aggregates, elements, venues, and Establishment of Recollection (Satipatthaana), we can know for sure that this Suttam is engaging in the ultimate way of teaching. And, as the ultimate way of teaching is indicative of Abhidhamma, we can establish the fact that this Suttam contains a segment or segments of Abhidhamma. For example, Mahaa Satipatthaana Suttam would easily qualify as Abhidhamma because this Suttam dedicates itself to teaching the establishment of recollection exclusively.
We can also find in the Suttams the teachings of persons and sentient beings so that they can also qualify as the conventional way of teaching. For example, Metta Suttam uses sentient beings as its objects while containing items of Abhidhamma such as gentleness (mettaa or adosa in Abhidhamma parlance).
Therefore, we now know that Suttanta Pitaka contains both the conventional way of teaching and the ultimate way of teaching. That is another way of saying that Suttams contains segments of Abhidhamma.
Now, let's take a closer look at the second paragraph we quoted earlier from Anangana Suttavannanaa.
The above paragraph is extremely significant in determining the goal of Suttanta Pitaka and Abhidhamma Pitaka.
The first sentence shows the conventional way of teaching and its purpose. And the purpose is the gain of unique insight. Unique insight is the right view that is sammaaditthi, which is an ultimate reality, or an item of Abhidhamma.
In short, Suttams not only contain segments of Abhidhamma, but also have the right view that is an item of Abhidhamma as their goal.
The second sentence solves the issue of whether Abhidhamma can deliver awakening at all. Yes, Abhidhamma can deliver the goods because "the Buddha delivers the ultimate way of teaching to those
who are capable of gaining unique insight by hearing the teachings in ultimate terms, penetating the meaning, and removing ignorance."