proposition: Lemma pair_add_monotone a b: a <= b -> (a <= a + b) && (a + b <= b).
proof: Proof. rewrite /pair_add /pair_le /= => h. by rewrite !mulnDr !mulnDl mulnC leq_add2l h (mulnC b.1) leq_add2r h. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq choice fintype order bigop ssralg) mathcomp(div ssrnum ssrint rat prime path binomial) mathcomp(tuple finset) gaia(fibm)