diff options
Diffstat (limited to 'theories/QArith/Qreduction.v')
| -rw-r--r-- | theories/QArith/Qreduction.v | 22 |
1 files changed, 19 insertions, 3 deletions
diff --git a/theories/QArith/Qreduction.v b/theories/QArith/Qreduction.v index c50c38b2..131214f5 100644 --- a/theories/QArith/Qreduction.v +++ b/theories/QArith/Qreduction.v @@ -93,11 +93,17 @@ Proof. Close Scope Z_scope. Qed. +Lemma Qred_eq_iff q q' : Qred q = Qred q' <-> q == q'. +Proof. + split. + - intros E. rewrite <- (Qred_correct q), <- (Qred_correct q'). + now rewrite E. + - apply Qred_complete. +Qed. + Add Morphism Qred : Qred_comp. Proof. - intros q q' H. - rewrite (Qred_correct q); auto. - rewrite (Qred_correct q'); auto. + intros. now rewrite !Qred_correct. Qed. Definition Qplus' (p q : Q) := Qred (Qplus p q). @@ -149,3 +155,13 @@ Theorem Qred_compare: forall x y, Proof. intros x y; apply Qcompare_comp; apply Qeq_sym; apply Qred_correct. Qed. + +Lemma Qred_le q q' : Qred q <= Qred q' <-> q <= q'. +Proof. + now rewrite !Qle_alt, <- Qred_compare. +Qed. + +Lemma Qred_lt q q' : Qred q < Qred q' <-> q < q'. +Proof. + now rewrite !Qlt_alt, <- Qred_compare. +Qed. |