proposition: Lemma morphim_Sylow G P : P \subset D -> Sylow G P -> Sylow (f @* G) (f @* P).
proof: Proof. by move=> sPD /andP[pP hallP]; rewrite /Sylow morphim_p_group // morphim_Hall. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)