proposition: Lemma injm_norm A : A \subset D -> f @* 'N(A) = 'N_(f @* D)(f @* A).
proof: Proof. move=> sAD; apply/eqP; rewrite -morphimIdom eqEsubset morphim_subnorm. rewrite -sub_morphpre_injm ?subsetIl // morphpreI injmK // setIS //. by rewrite -{2}(injmK sAD) morphpre_norm. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup)