proposition: Lemma ltn_logl p n : 0 < n -> logn p n < n.
proof: Proof. move=> n_gt0; have [p_gt1 | p_le1] := boolP (1 < p). by rewrite (leq_trans (ltn_expl _ p_gt1)) // dvdn_leq ?pfactor_dvdnn. by rewrite lognE (contraNF (@prime_gt1 _)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(fintype div bigop)