proposition: Lemma gal_eqP E {x y : gal_of E} : reflect {in E, x =1 y} (x == y).
proof: Proof. by rewrite -{1}(subfield_closed E); apply: aut_mem_eqP; apply: mem_repr_coset. 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)