Division in Numbers: factorisation of signatures

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12624 85f007b7-540e-0410-9357-904b9bb8a0f7

3 files changed, 3 insertions, 37 deletions

diff --git a/theories/Numbers/Integer/Abstract/ZDivEucl.v b/theories/Numbers/Integer/Abstract/ZDivEucl.v
index 2ec1cc9b0..e6af6f16f 100644
--- a/theories/Numbers/Integer/Abstract/ZDivEucl.v
+++ b/theories/Numbers/Integer/Abstract/ZDivEucl.v
@@ -26,21 +26,9 @@ Require Import ZAxioms ZProperties NZDiv.
 Open Scope NumScope.
 
 Module Type ZDiv (Import Z : ZAxiomsSig).
-
- Parameter Inline div : t -> t -> t.
- Parameter Inline modulo : t -> t -> t.
-
- Infix "/" := div : NumScope.
- Infix "mod" := modulo (at level 40, no associativity) : NumScope.
-
- Declare Instance div_wd : Proper (eq==>eq==>eq) div.
- Declare Instance mod_wd : Proper (eq==>eq==>eq) modulo.
-
+ Include Type NZDivCommon Z. (** div, mod, compat with eq, equation a=bq+r *)
  Definition abs z := max z (-z).
-
- Axiom div_mod : forall a b, b ~= 0 -> a == b*(a/b) + (a mod b).
  Axiom mod_always_pos : forall a b, 0 <= a mod b < abs b.
-
 End ZDiv.
 
 Module Type ZDivSig := ZAxiomsSig <+ ZDiv.
diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v
index 473631293..c152fa83e 100644
--- a/theories/Numbers/Integer/Abstract/ZDivFloor.v
+++ b/theories/Numbers/Integer/Abstract/ZDivFloor.v
@@ -29,20 +29,9 @@ Require Import ZAxioms ZProperties NZDiv.
 Open Scope NumScope.
 
 Module Type ZDiv (Import Z : ZAxiomsSig).
-
- Parameter Inline div : t -> t -> t.
- Parameter Inline modulo : t -> t -> t.
-
- Infix "/" := div : NumScope.
- Infix "mod" := modulo (at level 40, no associativity) : NumScope.
-
- Declare Instance div_wd : Proper (eq==>eq==>eq) div.
- Declare Instance mod_wd : Proper (eq==>eq==>eq) modulo.
-
- Axiom div_mod : forall a b, b ~= 0 -> a == b*(a/b) + (a mod b).
+ Include Type NZDivCommon Z. (** div, mod, compat with eq, equation a=bq+r *)
  Axiom mod_pos_bound : forall a b, 0 < b -> 0 <= a mod b < b.
  Axiom mod_neg_bound : forall a b, b < 0 -> b < a mod b <= 0.
-
 End ZDiv.
 
 Module Type ZDivSig := ZAxiomsSig <+ ZDiv.
diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v
index 2522f70c1..eca1e2ba1 100644
--- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v
+++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v
@@ -29,21 +29,10 @@ Require Import ZAxioms ZProperties NZDiv.
 Open Scope NumScope.
 
 Module Type ZDiv (Import Z : ZAxiomsSig).
-
- Parameter Inline div : t -> t -> t.
- Parameter Inline modulo : t -> t -> t.
-
- Infix "/" := div : NumScope.
- Infix "mod" := modulo (at level 40, no associativity) : NumScope.
-
- Declare Instance div_wd : Proper (eq==>eq==>eq) div.
- Declare Instance mod_wd : Proper (eq==>eq==>eq) modulo.
-
- Axiom div_mod : forall a b, b ~= 0 -> a == b*(a/b) + (a mod b).
+ Include Type NZDivCommon Z. (** div, mod, compat with eq, equation a=bq+r *)
  Axiom mod_bound : forall a b, 0<=a -> 0<b -> 0 <= a mod b < b.
  Axiom mod_opp_l : forall a b, b ~= 0 -> (-a) mod b == - (a mod b).
  Axiom mod_opp_r : forall a b, b ~= 0 -> a mod (-b) == a mod b.
-
 End ZDiv.
 
 Module Type ZDivSig := ZAxiomsSig <+ ZDiv.