proposition: Lemma pHall_subl pi G K H : H \subset K -> K \subset G -> pi.-Hall(G) H -> pi.-Hall(K) H.
proof: Proof. by move=> sHK sKG; rewrite /pHall sHK => /and3P[_ ->]; apply/pnat_dvd/indexSg. 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)