proposition: Lemma injm_Ldiv n A : f @* 'Ldiv_n(A) = 'Ldiv_n(f @* A).
proof: Proof. apply/eqP; rewrite eqEsubset morphim_Ldiv. rewrite -[f @* 'Ldiv_n(A)](morphpre_invm injf). rewrite -sub_morphim_pre; last by rewrite subIset ?morphim_sub. rewrite injmI ?injm_invm // setISS ?morphim_LdivT //. by rewrite sub_morphim_pre ?morphim_sub // morphpre_invm. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism action) mathcomp(quotient gfunctor gproduct ssralg countalg finalg zmodp) mathcomp(cyclic pgroup gseries nilpotent sylow)