diff options
Diffstat (limited to 'theories/Numbers/Integer/Binary/ZBinary.v')
| -rw-r--r-- | theories/Numbers/Integer/Binary/ZBinary.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Numbers/Integer/Binary/ZBinary.v b/theories/Numbers/Integer/Binary/ZBinary.v index acc77b3e7..0ff896367 100644 --- a/theories/Numbers/Integer/Binary/ZBinary.v +++ b/theories/Numbers/Integer/Binary/ZBinary.v @@ -10,7 +10,7 @@ (*i $Id$ i*) -Require Import ZTimesOrder. +Require Import ZMulOrder. Require Import ZArith. Open Local Scope Z_scope. @@ -25,7 +25,7 @@ Definition NZ0 := 0. Definition NZsucc := Zsucc'. Definition NZpred := Zpred'. Definition NZadd := Zplus. -Definition NZminus := Zminus. +Definition NZsub := Zminus. Definition NZmul := Zmult. Theorem NZeq_equiv : equiv Z NZeq. @@ -54,7 +54,7 @@ Proof. congruence. Qed. -Add Morphism NZminus with signature NZeq ==> NZeq ==> NZeq as NZminus_wd. +Add Morphism NZsub with signature NZeq ==> NZeq ==> NZeq as NZsub_wd. Proof. congruence. Qed. @@ -89,12 +89,12 @@ Proof. intros; do 2 rewrite <- Zsucc_succ'; apply Zplus_succ_l. Qed. -Theorem NZminus_0_r : forall n : Z, n - 0 = n. +Theorem NZsub_0_r : forall n : Z, n - 0 = n. Proof. exact Zminus_0_r. Qed. -Theorem NZminus_succ_r : forall n m : Z, n - (NZsucc m) = NZpred (n - m). +Theorem NZsub_succ_r : forall n m : Z, n - (NZsucc m) = NZpred (n - m). Proof. intros; rewrite <- Zsucc_succ'; rewrite <- Zpred_pred'; apply Zminus_succ_r. @@ -213,11 +213,11 @@ Qed. End ZBinAxiomsMod. -Module Export ZBinTimesOrderPropMod := ZTimesOrderPropFunct ZBinAxiomsMod. +Module Export ZBinMulOrderPropMod := ZMulOrderPropFunct ZBinAxiomsMod. (** Z forms a ring *) -(*Lemma Zring : ring_theory 0 1 NZadd NZmul NZminus Zopp NZeq. +(*Lemma Zring : ring_theory 0 1 NZadd NZmul NZsub Zopp NZeq. Proof. constructor. exact Zadd_0_l. |