proposition: Lemma a_grows2 m n : a m < a (m + n.+1).
proof: Proof. elim: n => [| n ihn] /=; first by rewrite addn1 a_grows1. by apply: ltn_trans ihn _; rewrite !addnS a_grows1. Qed.
imports: mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial