Fact fixedField_is_aspace E (A : {set gal_of E}) : is_aspace (fixedField A).
Canonical fixedField_aspace E A : {subfield L} :=
ASpace (@fixedField_is_aspace E A).

(* Specifications: *)
Lemma fixedField_bound E (A : {set gal_of E}) : (fixedField A <= E)%VS.
Lemma galois_connection_subv K E :
(K <= E)%VS -> (K <= fixedField ('Gal(E / K)))%VS.
Lemma galois_connection_subset E (A : {set gal_of E}):
A \subset 'Gal(E / fixedField A).
Lemma galois_connection K E (A : {set gal_of E}):
(K <= E)%VS -> (A \subset 'Gal(E / K)) = (K <= fixedField A)%VS.