فَعَلَ رَبُّكَ بِأَصْحَابِ الْفِيلِ
How your Lord dealt with the people of the elephant. (الفيل: 1)
The possessive address in rabbuka draws the audience personally into a reminder of divine care and power. It is a feature of address and thematic relevance, not a change in the dictionary meaning of rabb.
The choice is fitting to the surah’s purpose. Yet every possessive pronoun does not produce formal restriction, and direct address does not by itself establish an exclusive relation. The inference must be limited to what the context supports.
Aṣḥāb al-fīl identifies the group by a recognizable association; not every unmentioned historical detail is technical ellipsis.