Shiites prove in their Books that Imam Ali used to pray behind Abu Bakr.
Shiites claim that an infallible Imam would never pray before a non-infallible Imam.
Yet, in al-Ihtejaj by Tabrasi, Page 94, Vol 1, al Aalami, Beirut, Lebanon. it is narrated that Imam Ali prayed behind Abu Bakr.
The sane Riwaya is reported in Ilalu Asharae'i by As-Sadouk.
Now: If Ali prayed behind Abu Bakr, it means Ali acknowledged, though tacitly, that Abu Bakr was better than him!
At the very least, Ali recognized that Abu Bakr was a pious Muslim since prayer behind a Kaffer wouldn't be valid.
Conclusion: The entire Shiite perception of the relations between Ahlul-Bayt and the Sahaba is untrue.