Section SeparablePoly.
Variable R : idomainType.
Implicit Types p q d u v : {poly R}.
Definition separable_poly p := coprimep p p^`().
Local Notation separable := separable_poly.
Local Notation lcn_neq0 := (Pdiv.Idomain.lc_expn_scalp_neq0 _).

Lemma separable_prod_XsubC (r : seq R) :
separable (\prod_(x <- r) ('X - x%:P)) = uniq r.