proposition: Lemma injm_Aut_full : (Aut_in (Aut (f @* G)) (f @* H) \isog Aut (f @* H)) = (Aut_in (Aut G) H \isog Aut H).
proof: Proof. by rewrite (isog_transl _ injm_Aut_sub) (isog_transr _ (injm_Aut injf sHD)). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)