proposition: Fact lt_rat_def x y : (lt_rat x y) = (y != x) && (le_rat x y).
proof: Proof. by rewrite lt_ratE le_ratE lt_def rat_eq. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg countalg div ssrnum) mathcomp(ssrint prime archimedean)