diff options
| author | emakarov | 2007-11-14 19:47:46 +0000 |
|---|---|---|
| committer | emakarov | 2007-11-14 19:47:46 +0000 |
| commit | 87bfa992d0373cd1bfeb046f5a3fc38775837e83 (patch) | |
| tree | 5a222411c15652daf51a6405e2334a44a9c95bea /theories/Numbers/Integer/Binary | |
| parent | d04ad26f4bb424581db2bbadef715fef491243b3 (diff) | |
Update on Numbers; renamed ZOrder.v to ZLt to remove clash with ZArith/Zorder on MacOS.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10323 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Integer/Binary')
| -rw-r--r-- | theories/Numbers/Integer/Binary/ZBinary.v | 29 |
1 files changed, 23 insertions, 6 deletions
diff --git a/theories/Numbers/Integer/Binary/ZBinary.v b/theories/Numbers/Integer/Binary/ZBinary.v index 3c680ec918..96e01a731c 100644 --- a/theories/Numbers/Integer/Binary/ZBinary.v +++ b/theories/Numbers/Integer/Binary/ZBinary.v @@ -100,14 +100,14 @@ intros; rewrite <- Zsucc_succ'; rewrite <- Zpred_pred'; apply Zminus_succ_r. Qed. -Theorem NZtimes_0_r : forall n : Z, n * 0 = 0. +Theorem NZtimes_0_l : forall n : Z, 0 * n = 0. Proof. -exact Zmult_0_r. +reflexivity. Qed. -Theorem NZtimes_succ_r : forall n m : Z, n * (NZsucc m) = n * m + n. +Theorem NZtimes_succ_l : forall n m : Z, (NZsucc n) * m = n * m + m. Proof. -intros; rewrite <- Zsucc_succ'; apply Zmult_succ_r. +intros; rewrite <- Zsucc_succ'; apply Zmult_succ_l. Qed. End NZAxiomsMod. @@ -137,7 +137,7 @@ Proof. congruence. Qed. -Theorem NZle_lt_or_eq : forall n m : Z, n <= m <-> n < m \/ n = m. +Theorem NZlt_eq_cases : forall n m : Z, n <= m <-> n < m \/ n = m. Proof. intros n m; split. apply Zle_lt_or_eq. intro H; destruct H as [H | H]. now apply Zlt_le_weak. rewrite H; apply Zle_refl. @@ -148,7 +148,7 @@ Proof. exact Zlt_irrefl. Qed. -Theorem NZlt_succ_le : forall n m : Z, n < (NZsucc m) <-> n <= m. +Theorem NZlt_succ_r : forall n m : Z, n < (NZsucc m) <-> n <= m. Proof. intros; unfold NZsucc; rewrite <- Zsucc_succ'; split; [apply Zlt_succ_le | apply Zle_lt_succ]. @@ -215,6 +215,23 @@ End ZBinAxiomsMod. Module Export ZBinTimesOrderPropMod := ZTimesOrderPropFunct ZBinAxiomsMod. +(** Z forms a ring *) + +(*Lemma Zring : ring_theory 0 1 NZplus NZtimes NZminus Zopp NZeq. +Proof. +constructor. +exact Zplus_0_l. +exact Zplus_comm. +exact Zplus_assoc. +exact Ztimes_1_l. +exact Ztimes_comm. +exact Ztimes_assoc. +exact Ztimes_plus_distr_r. +intros; now rewrite Zplus_opp_minus. +exact Zplus_opp_r. +Qed. + +Add Ring ZR : Zring.*) |