What should a worshiper do if he intended to pray Dhuhr, but then realized it was Asr while performing it, and is he required to interrupt his prayer and repeat the takbirat al-ihram?

If someone prays Dhuhr and then joins a congregational Asr prayer by mistake, intending Dhuhr, and then remembers during the prayer that it is Asr, it is not permissible for him to change his intention to Asr. Rather, he should break his prayer, then say "Allahu Akbar" (the takbirat al-ihram) and rejoin the Imam with the intention of Asr, because intention is a condition for the validity of prayer. However, if he has not prayed Dhuhr and enters the mosque while they are praying Asr, he should pray with them with the intention of Dhuhr, and then pray Asr afterwards due to the obligation of sequential order. The difference in intention between the Imam and the follower does not cause any harm in this case.