Halachik Conclusion:
List the proofs the Rif brings as to why he concludes lhalacha in accordance with the רבנן?
https://hebrewbooks.org/pdfpager.aspx?req=37953&st=&pgnum=580
https://hebrewbooks.org/pdfpager.aspx?req=37953&st=&pgnum=581
List how the Ran refutes all the proofs of the Rif.
See new source – Learn ר”ן דף טז. דפי הריף “ומנא לן
https://hebrewbooks.org/pdfpager.aspx?req=37953&st=&pgnum=581
Learn the רא”ש who brings the different opinions whether we rule like Rabanan or like chanania
Learn רא”ש פרק ג ס’ א
https://hebrewbooks.org/pdfpager.aspx?req=37953&st=&pgnum=350
https://hebrewbooks.org/pdfpager.aspx?req=37953&st=&pgnum=351
https://hebrewbooks.org/pdfpager.aspx?req=37953&st=&pgnum=352