proposition: Lemma injm_Aut_sub : Aut_in (Aut (f @* G)) (f @* H) \isog Aut_in (Aut G) H.
proof: Proof. do 2!rewrite isog_sym (isog_transl _ (Aut_in_isog _ _)). by rewrite isog_sym (isom_isog _ _ restr_perm_isom) // restr_perm_Aut. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)