proposition: Lemma galois_connection_subv K E : (K <= E)%VS -> (K <= fixedField ('Gal(E / K)))%VS.
proof: Proof. move=> sKE; apply/subvP => a Ka; have Ea := subvP sKE a Ka. by apply/fixedFieldP=> // x galEx; apply: (fixed_gal sKE). 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)