proposition: Lemma p_rank_witness p G : {E | E \in 'E_p^('r_p(G))(G)}.
proof: Proof. have [E EG_E mE]: {E | E \in 'E_p(G) & 'r_p(G) = logn p #|E| }. by apply: eq_bigmax_cond; rewrite (cardD1 1%G) inE sub1G abelem1. by exists E; rewrite inE EG_E -mE /=. 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)