What is meant by "al-hujjah" (the argument/proof) in the interpretation of Allah's saying: "Indeed, there is no authority for him over those who believe and rely upon their Lord. His authority is only over those who take him as an ally and those who associate partners with Him"?

What is meant by "proof" (hujjah) is the sound evidence, not the weak. The authority (sultan) that Satan has over the people of misguidance is his domination over them through enticement and incitement, as in the Almighty's saying: "His authority is only over those who take him as an ally and those who associate partners with Him." As for the authority denied to Satan, it is the authority of proof and evidence. He had no sound proof over his followers; rather, he deceived them with weak arguments. Ibn al-Qayyim clarifies that the established authority is Satan's control over them, while the denied authority is the authority of proof; for Satan gained power over them through their will and choice, not by his own strength.