proposition: Lemma gal_generated E (A : {set gal_of E}) : 'Gal(E / fixedField A) = <<A>>.
proof: Proof. apply/eqP; rewrite eqEsubset gen_subG galois_connection_subset. by rewrite -[<<A>>]gal_fixedField galS // 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)