proposition: Lemma galTrace_fixedField a : a \in E -> galTrace K E a \in fixedField 'Gal(E / K).
proof: Proof. move=> Ea; apply/fixedFieldP=> [|x galEx]. by apply: rpred_sum => x _; apply: memv_gal. rewrite {2}/galTrace (reindex_acts 'R _ galEx) ?astabsR //=. by rewrite rmorph_sum; apply: eq_bigr => y _; rewrite galM ?lfunE. 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)