proposition: Lemma fixedFieldP E {A : {set gal_of E}} a : a \in E -> reflect (forall x, x \in A -> x a = a) (a \in fixedField A).
proof: Proof. by rewrite memv_cap => ->; apply: (iffP subv_bigcapP) => cAa x /cAa/fixedSpaceP. 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)