proposition: Lemma mem_fixedFieldP E (A : {set gal_of E}) a : a \in fixedField A -> a \in E /\ (forall x, x \in A -> x a = a).
proof: Proof. by move=> fixAa; have [Ea _] := memv_capP fixAa; have:= fixedFieldP Ea fixAa. 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)