proposition: Lemma p_rank_geP p n G : reflect (exists E, E \in 'E_p^n(G)) (n <= 'r_p(G)).
proof: Proof. apply: (iffP idP) => [|[E]]; last first. by rewrite inE => /andP[Ep_E /eqP <-]; rewrite (bigmax_sup E). have [D /pnElemP[sDG abelD <-]] := p_rank_witness p G. by case/abelem_pnElem=> // E; exists E; apply: (subsetP (pnElemS _ _ sDG)). 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)