proposition: Lemma injm_nil G : 'injm f -> G \subset D -> nilpotent (f @* G) = nilpotent G.
proof: Proof. move=> injf sGD; apply/idP/idP; last exact: morphim_nil. case/ucnP=> n; rewrite -injm_ucn // => /injm_morphim_inj defZ. by apply/ucnP; exists n; rewrite defZ ?gFsub_trans. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(fintype div bigop prime finset fingroup morphism) mathcomp(automorphism quotient commutator gproduct) mathcomp(gfunctor center gseries cyclic)