Section NatConst.
Variables (I : finType) (A : pred I).
Arguments bigmax_eq_arg [I] i0 [P F].
Arguments biglcmn_sup [I] i0 [P F m].

Lemma dvdn_biggcdP (I : finType) (P : pred I) F m :
reflect (forall i, P i -> m %| F i) (m %| \big[gcdn/0]_(i | P i) F i).