Fact lt_rat_def x y : (lt_rat x y) = (y != x) && (le_rat x y).

(* Specifications: *)
Lemma numq_le0 x : (numq x <= 0) = (x <= 0).
Lemma denq_mulr_sign (b : bool) x : denq ((-1) ^+ b * x) = denq x.
Canonical archiType := ArchiFieldType rat rat_archimedean.