what is the definition of Ahl ul Bayt

There are numerous proofs present from the Quran in this thread. Please pick one and point out why you fail to see it as a proof.

[2:111] Say: Bring your proof if you are truthful.

Could you show us a Hadith where the Prophet (saww) is stating that all the Bani Hashim are his Ahlul Bayt, for whom the verse of purification was decended?

What are your views about the Hadiths in Saha Sitta where its clearly stated that the verse of Tatheer (in praise of Ahlul Bayt (as)) is for Panjatan Paak exclusively?

And since your area of speciality seems to be Islamic history, did Bani Hashim and Aulad e Aqeel (may Allah bless him) considered themselves equal to the Panjatan Paak since you consider them all part of the Ahlul Bayt (as)?
Thanks