I am studying research paper " A note on Tanguy Rivoal and Wadim Zudilin"

I couldn't think about how authors write the equation - we obtain $\phi_{(n) }^{-1} ( F(t) (t+m)^5 )_{ t=-m} $ $ \epsilon $(belongs to) integers for m= 0 ,1,...,n by defininig $\phi_{(n)} = \prod^{2√n<p\leq n } p^{\rho_0(n/p) } $ .Please see last 3-4 lines of image posted below

I have understood everything in research paper till this argument and I don't know how autors derives this.

I think they are using [12, lemma1] (Paper-" One of odd zeta values from $\zeta(5)$ to $\zeta(25) $ is irrational by elementary means " By Wadim Zudilin )whose image I am posting below but I am not able to obtain this relation from the lemma. Image of lemma ->

Can someone please help how to deduce this equation $\phi_{(n) }^{-1} ( F(t) (t+m)^5 )_{ t=-m} $ $\epsilon$(belongs to) integers.