diff options
| author | letouzey | 2010-01-07 15:32:46 +0000 |
|---|---|---|
| committer | letouzey | 2010-01-07 15:32:46 +0000 |
| commit | e3e6ff629e258269bc9fe06f7be99a2d5f334071 (patch) | |
| tree | e8812c6d9da2b90beee23418dd2d69995f144ec7 /theories/Numbers/Cyclic/Abstract | |
| parent | e1059385b30316f974d47558d8b95b1980a8f1f8 (diff) | |
Numbers: separation of funs, notations, axioms. Notations via module, without scope.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12639 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Cyclic/Abstract')
| -rw-r--r-- | theories/Numbers/Cyclic/Abstract/NZCyclic.v | 20 |
1 files changed, 8 insertions, 12 deletions
diff --git a/theories/Numbers/Cyclic/Abstract/NZCyclic.v b/theories/Numbers/Cyclic/Abstract/NZCyclic.v index e3c14879df..517e48ad9c 100644 --- a/theories/Numbers/Cyclic/Abstract/NZCyclic.v +++ b/theories/Numbers/Cyclic/Abstract/NZCyclic.v @@ -43,17 +43,13 @@ Definition add := w_op.(znz_add). Definition sub := w_op.(znz_sub). Definition mul := w_op.(znz_mul). -Delimit Scope NumScope with Num. -Bind Scope NumScope with t. -Local Open Scope NumScope. -Notation "x == y" := (eq x y) (at level 70) : NumScope. -Notation "0" := zero : NumScope. -Notation S := succ. -Notation P := pred. -Notation "x + y" := (add x y) : NumScope. -Notation "x - y" := (sub x y) : NumScope. -Notation "x * y" := (mul x y) : NumScope. - +Local Infix "==" := eq (at level 70). +Local Notation "0" := zero. +Local Notation S := succ. +Local Notation P := pred. +Local Infix "+" := add. +Local Infix "-" := sub. +Local Infix "*" := mul. Hint Rewrite w_spec.(spec_0) w_spec.(spec_succ) w_spec.(spec_pred) w_spec.(spec_add) w_spec.(spec_mul) w_spec.(spec_sub) : w. @@ -129,7 +125,7 @@ rewrite <- pred_mod_wB. replace ([| n |] + 1 - 1)%Z with [| n |] by auto with zarith. apply NZ_to_Z_mod. Qed. -Lemma Z_to_NZ_0 : Z_to_NZ 0%Z == 0%Num. +Lemma Z_to_NZ_0 : Z_to_NZ 0%Z == 0. Proof. unfold NZ_to_Z, Z_to_NZ. wsimpl. rewrite znz_of_Z_correct; auto. |