proposition: Lemma le_ratE x y : le_rat x y = (numq x * denq y <= numq y * denq x).
proof: Proof. by case: x; case: y. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg countalg div ssrnum) mathcomp(ssrint prime archimedean)