proposition: Lemma p_rank_pmaxElem_exists p r G : 'r_p(G) >= r -> exists2 E, E \in 'E*_p(G) & 'r_p(E) >= r.
proof: Proof. case/p_rank_geP=> D /setIdP[EpD /eqP <- {r}]. have [E EpE sDE] := pmaxElem_exists EpD; exists E => //. case/pmaxElemP: EpE => /setIdP[_ abelE] _. by rewrite (p_rank_abelem abelE) lognSg. 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)