proposition: Lemma p_rank_Sylow p G H : p.-Sylow(G) H -> 'r_p(H) = 'r_p(G).
proof: Proof. move=> sylH; apply/eqP; rewrite eqn_leq (p_rankS _ (pHall_sub sylH)) /=. apply/bigmax_leqP=> E /[1!inE] /andP[sEG abelE]. have [P sylP sEP] := Sylow_superset sEG (abelem_pgroup abelE). have [x _ ->] := Sylow_trans sylP sylH. by rewrite p_rankJ -(p_rank_abelem abelE) (p_rankS _ sEP). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism action) mathcomp(quotient gfunctor gproduct ssralg countalg finalg zmodp) mathcomp(cyclic pgroup gseries nilpotent sylow)