رَجُلٌ حَسَنُ الْوَجْهِ
Translation: A man with a handsome face.
Ḥasanu l-wajhi is a formal (lafẓī) iḍāfah; it does not automatically make ḥasanu definite.
Definiteness here belongs to semantic iḍāfah.
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Semantic vs. Formal Iḍāfah
Conclusion: Definite and Indefinite Nouns
رَجُلٌ حَسَنُ الْوَجْهِ
Translation: A man with a handsome face.
Ḥasanu l-wajhi is a formal (lafẓī) iḍāfah; it does not automatically make ḥasanu definite.
Definiteness here belongs to semantic iḍāfah.