I finally understand what the "proof" is that Shenhua's father was talking about. Ryo had to prove that he was "the one" who held the pheonix and that his mirror was legit.
See....only the REAL Pheonix mirror could activate elaborate mechanism revealing the giant mirrors. And since the design on the giant mirrors look EXACTLY like the small real ones.. Shenhua can cross check them against Ryo's mirror to prove it's indeed one of the original mirrors.
Shenhua's father basically set up a device which would prove that Ryo was the "one" referred to in the poem of Bailu Village! He had to set up the contraption so his daughter could follow Ryo with his permission and full confidence.
He also knew that the sword was the "key" needed to unlock the mirror pedestal.. he knew that the spirit of Shenhua's ancestors was contained in the sword (since it's the sword of 7 stars and Shenhua prays to her ancestors by looking up to the big dipper)) and that Shenhua had the power to insert it since she has the power of her ancestors.
Shenhua's father basically created a two part puzzle.... one only Shenhua could activate with her powers and the other only Ryo could activate with his mirror.