proposition: Lemma fixedFieldS E (A B : {set gal_of E}) : A \subset B -> (fixedField B <= fixedField A)%VS.
proof: Proof. move/subsetP=> sAB; apply/subvP => a /mem_fixedFieldP[Ea cBa]. by apply/fixedFieldP; last apply: sub_in1 cBa. 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)