proposition: Lemma fixedField_galois E (A : {set gal_of E}): galois (fixedField A) E.
proof: Proof. have: galois (fixedField <<A>>) E. by apply/galois_fixedField; rewrite gal_fixedField. by apply: galoisS; rewrite capvSl fixedFieldS // subset_gen. 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)