Fact ratr_is_rmorphism : rmorphism (@ratr F).Canonical ratr_additive := Additive ratr_is_rmorphism.Canonical ratr_rmorphism := RMorphism ratr_is_rmorphism.

(* Specifications: *)
Lemma ler0q x : (0 <= ratr F x) = (0 <= x).
Lemma lerq0 x : (ratr F x <= 0) = (x <= 0).
Lemma ltr0q x : (0 < ratr F x) = (0 < x).
Lemma ltrq0 x : (ratr F x < 0) = (x < 0).
Lemma ratr_sg x : ratr F (sgr x) = sgr (ratr F x).
Lemma rat_ring_theory : (ring_theory 0%Q 1%Q addq mulq subq oppq eq).
Lemma rat_field_theory : Field_theory.field_theory 0%Q 1%Q addq mulq subq oppq divq invq eq.