proposition: Lemma rank_Ohm1 G : 'r('Ohm_1(G)) = 'r(G).
proof: Proof. apply/eqP; rewrite eqn_leq rankS ?Ohm_sub //. by have [p _ ->] := rank_witness G; rewrite -p_rank_Ohm1 p_rank_le_rank. 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)