What is the ruling on a disobedient person who persists in his disobedience after proof has been established against him, and what is the evidence for it?

The doctrine of Ahl al-Sunnah wa al-Jama’ah is that a sinner is not a disbeliever. If he dies while engaged in sin, then his fate is subject to Allah’s will. If He wills, He may forgive him and admit him to Paradise. If He wills, He may admit him to Hellfire, but he will not remain therein eternally. The proofs for this include the Almighty’s saying: "Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills," and the hadith: "Whoever dies without associating anything with Allah will enter Paradise, even if he stole or committed adultery." This applies to one who does not deem the sin permissible; if he deems it permissible, then he is a disbeliever.