proposition: Lemma rat_in_P_ge1 x: rat_in_P x -> 1 <= x.
proof: Proof. by move/rat_in_PP => [n ->]; rewrite ler1n. 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)