proposition: Lemma pquotient_pHall : K <| G -> K <| H -> pi.-Hall(G / K) (H / K) = pi.-Hall(G) H.
proof: Proof. case/andP=> sKG nKG; case/andP=> sKH nKH. by rewrite pmorphim_pHall // ker_coset /psubgroup subsetI sKH sKG. 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)