proposition: Lemma pair_add_smonotone a b: a < b -> (a < a + b) && (a + b < b).
proof: Proof. rewrite /pair_add /pair_lt /= => h. by rewrite !mulnDr !mulnDl mulnC ltn_add2l h (mulnC b.1) ltn_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)