proposition: Lemma small_nil_class G : nil_class G <= 5 -> nilpotent G.
proof: Proof. move=> leK5; case: (ltnP 5 #|G|) => [lt5G | leG5 {leK5}]. by rewrite nilpotent_class (leq_ltn_trans leK5). apply: pgroup_nil (pdiv #|G|) _ _; apply/andP; split=> //. by case: #|G| leG5 => //; do 5!case=> //. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype prime bigop finset fingroup morphism) mathcomp(automorphism quotient action cyclic gproduct) mathcomp(gfunctor commutator pgroup center nilpotent)