proposition: Lemma galois_connection K E (A : {set gal_of E}): (K <= E)%VS -> (A \subset 'Gal(E / K)) = (K <= fixedField A)%VS.
proof: Proof. move=> sKE; apply/idP/idP => [/fixedFieldS | /(galS E)]. exact/subv_trans/galois_connection_subv. exact/subset_trans/galois_connection_subset. 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)