proposition: Lemma ltfn3n n : 0 < n -> f n < 3 * n.
proof: Proof. move=> n_gt0. have := leqfn3n n; rewrite leq_eqVlt; case: eqP => // fnE _. have : 3 * n < f (3 * n) by apply: ltnfn; rewrite muln_gt0. by rewrite -[in X in _ < X -> _]fnE ffE ltnn. Qed.
imports: mathcomp(all_ssreflect)