proposition: Lemma Ohm1_eq1 G : ('Ohm_1(G) == 1) = (G :==: 1).
proof: Proof. apply/idP/idP => [/eqP G1_1 | /eqP->]; last by rewrite -subG1 Ohm_sub. by rewrite -(setIid G) TI_Ohm1 // G1_1 setIg1. 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)