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diff --git a/theories/Num/Definitions.v b/theories/Num/Definitions.v
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+(*i $Id $ i*)
+
+(*s 
+  Axiomatisation of a numerical set 
+  It will be instantiated by Z and R later on
+  We choose to introduce many operation to allow flexibility in definition 
+  ([S] is primitive in the definition of [nat] while [add] and [one] 
+   are primitive in the definition 
+*)
+
+Parameter N:Type.
+Parameter zero:N.
+Parameter one:N.
+Parameter add:N->N->N.
+Parameter S:N->N.
+
+(*s Relations *)
+Parameter eq,lt,le,gt,ge:N->N->Prop.    
+Definition neq [x,y:N] := (eq x y)->False.
+