proposition: Lemma p_rank_le_rank p G : 'r_p(G) <= 'r(G).
proof: Proof. case: (posnP 'r_p(G)) => [-> //|]; rewrite p_rank_gt0 mem_primes. case/and3P=> p_pr _ pG; have lepg: p < #|G|.+1 by rewrite ltnS dvdn_leq. by rewrite ['r(G)]big_mkord (bigmax_sup (Ordinal lepg)). 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)