Prenex Implicits gal_repr.

(* Specifications: *)
Lemma gal_eqP E {x y : gal_of E} : reflect {in E, x =1 y} (x == y).
Lemma galK E (f : 'AEnd(L)) : (f @: E <= E)%VS -> {in E, gal E f =1 f}.
Lemma eq_galP E (f g : 'AEnd(L)) :
(f @: E <= E)%VS -> (g @: E <= E)%VS ->
reflect {in E, f =1 g} (gal E f == gal E g).
Lemma limg_gal E (x : gal_of E) : (x @: E)%VS = E.
Lemma galV E (x : gal_of E) : {in E, (x^-1)%g =1 x^-1%VF}.
Definition galoisG V U := gal V @* <<kAEnd (U :&: V) V>>.