proposition: Lemma p_rank_Hall pi p G H : pi.-Hall(G) H -> p \in pi -> 'r_p(H) = 'r_p(G).
proof: Proof. move=> hallH pi_p; have [P sylP] := Sylow_exists p H. by rewrite -(p_rank_Sylow sylP) (p_rank_Sylow (subHall_Sylow hallH pi_p sylP)). 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)