proposition: Lemma logn_prime p q : prime q -> logn p q = (p == q).
proof: Proof. move=> pr_q; have q_gt0 := prime_gt0 pr_q; rewrite lognE q_gt0 /=. case pr_p: (prime p); last by case: eqP pr_p pr_q => // -> ->. by rewrite dvdn_prime2 //; case: eqP => // ->; rewrite divnn q_gt0 logn1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(fintype div bigop)