fact: Definition le_rat '(Rat x _) '(Rat y _) := x.1 * y.2 <= y.1 * x.2.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg countalg div ssrnum) mathcomp(ssrint prime archimedean)