Hazrat Mahdi (as) will definitely appear

Even if only one day of the world remained, Allah would extend that day until he [Hazrat Mahdi (as)] takes power. (Al-Muttaqi al-Hindi, Al-Burhan fi Alamat al-Mahdi Akhir az-Zaman, p. 10)

If it were the last day of life, Allah would prolong that day until He sends a man [Hazrat Mahdi (as)] from my Household. (Al-Muttaqi al-Hindi, Al-Burhan fi Alamat al-Mahdi Akhir az-Zaman, p. 10)

Hazrat Mahdi (as) will come from among my community… In his time, my community will be blessed with a blessing the like of which has never been seen before. Much rain will fall down from the sky, and the plants of the ground will hold back nothing. (Al-Muttaqi al-Hindi, Al-Burhan fi Alamat al-Mahdi Akhir az-Zaman, p. 9)

Even if only one night remained for the world, Allah would extend it, so that one from my House would come and rule the world. His name matches mine, and his father’s name my father’s name. Just as the world was filled with cruelty, he will fill it with justice. (Al-Muttaqi al-Hindi, Al-Burhan fi Alamat al-Mahdi Akhir az-Zaman, p. 11)