diff options
Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZDivFloor.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivFloor.v | 13 |
1 files changed, 1 insertions, 12 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v index 4736312939..c152fa83ea 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. |