proposition: Lemma morphim_Hall G H : H \subset D -> Hall G H -> Hall (f @* G) (f @* H).
proof: Proof. by move=> sHD /HallP[pi piH]; apply: (@pHall_Hall _ pi); apply: morphim_pHall. 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)