proposition: Lemma galK E (f : 'AEnd(L)) : (f @: E <= E)%VS -> {in E, gal E f =1 f}.
proof: Proof. rewrite -kAut1E -{1 2}(subfield_closed E) => autEf. apply: (aut_mem_eqP (mem_repr_coset _) _ (eqxx _)). by rewrite subgK /= ?(mem_kAut_coset autEf) // ?mem_quotient ?inE. 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)