diff options
Diffstat (limited to 'theories/Numbers/Integer/NatPairs/ZNatPairs.v')
| -rw-r--r-- | theories/Numbers/Integer/NatPairs/ZNatPairs.v | 27 |
1 files changed, 9 insertions, 18 deletions
diff --git a/theories/Numbers/Integer/NatPairs/ZNatPairs.v b/theories/Numbers/Integer/NatPairs/ZNatPairs.v index 02f73f4d1..2ca4bc5d8 100644 --- a/theories/Numbers/Integer/NatPairs/ZNatPairs.v +++ b/theories/Numbers/Integer/NatPairs/ZNatPairs.v @@ -1,21 +1,12 @@ -Require Import NDomain. -Require Import NAxioms. -Require Import NPlus. -Require Import NTimes. -Require Import NLt. -Require Import NPlusLt. -Require Import NTimesLt. - -Require Import ZDomain. -Require Import ZAxioms. -Require Import ZPlus. -Require Import ZTimes. -Require Import ZOrder. -Require Import ZPlusOrder. -Require Import ZTimesOrder. - -Module NatPairsDomain (NPlusModule : NPlus.PlusSignature) <: - ZDomain.DomainSignature. +Require Export NTimesLt. +Require Export ZTimesOrder. + +Module NatPairsDomain (Export NPlusModule : NPlus.PlusSignature) : + ZDomain.DomainSignature + with Definition Z := (N * N)%type. + with Definition E (p1 p2 : Z) := ((fst p1) + (snd p2) == (fst p2) + (snd p1))%Nat. + with Definition e (p1 p2 : Z) := e ((fst p1) + (snd p2)) ((fst p2) + (snd p1))%Nat. + Module Export NPlusPropertiesModule := NPlus.PlusProperties NPlusModule. Definition Z : Set := (N * N)%type. |