proposition: Lemma kAEnd_norm K E : kAEnd K E \subset 'N(kAEndf E)%g.
proof: Proof. apply/subsetP=> x; rewrite -groupV 2!in_set => /andP[_ /eqP ExE]. apply/subsetP=> _ /imsetP[y homEy ->]; rewrite !in_set !kAutfE in homEy *. apply/kAHomP=> u Eu; have idEy := kAHomP homEy; rewrite -ExE in idEy. rewrite !(@lfunE _ _ L) /= (@lfunE _ _ L) /= idEy ?memv_img //. by rewrite lker0_lfunVK ?AEnd_lker0. 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)