proposition: Lemma gal_independent E (P : pred (gal_of E)) (c_ : gal_of E -> L) : (forall a, a \in E -> \sum_(x | P x) c_ x * x a = 0) -> (forall x, P x -> c_ x = 0).
proof: Proof. move=> sum_cP_0 x Px; apply/eqP/idPn=> /(gal_independent_contra Px)[a Ea]. by rewrite sum_cP_0 ?eqxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop ssralg poly) mathcomp(polydiv finset fingroup morphism quotient perm) mathcomp(action zmodp cyclic matrix mxalgebra vector) mathcomp(falgebra fieldext separable)