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diff --git a/theories/Num/Axioms.v b/theories/Num/Axioms.v
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+(*i $Id: i*)
+
+(*s Axioms for the basic numerical operations *)
+Require Export Definitions.
+Require Export NSyntax.
+
+(*s Axioms for [eq] *)
+
+Axiom eq_refl : (x:N)(x=x).
+Axiom eq_sym : (x,y:N)(x=y)->(y=x).
+Axiom eq_trans : (x,y,z:N)(x=y)->(y=z)->(x=z).
+
+(*s Axioms for [add] *)
+
+Axiom add_sym : (x,y:N)(x+y)=(y+x).
+Axiom add_eq_compat : (x1,x2,y1,y2:N)(x1=x2)->(y1=y2)->(x1+y1)=(x2+y2).
+Axiom add_assoc_l : (x,y,z:N)((x+y)+z)=(x+(y+z)).
+Axiom add_x_0 : (x:N)(x+zero)=x.
+
+(*s Axioms for [S] *)
+Axiom S_eq_compat : (x,y:N)(x=y)->(S x)=(S y).
+Axiom add_Sx_y : (x,y:N)((S x)+y)=(S (x+y)).
+
+(*s Axioms for [one] *)
+Axiom S_0_1 : (S zero)=one.
+
+(*s Axioms for [<], 
+    properties of [>], [<=] and [>=] will be derived from [<] *)
+
+Axiom lt_trans : (x,y,z:N)x<y->y<z->x<z.
+Axiom lt_anti_sym : (x,y:N)x<y->~(y<x).
+
+Axiom lt_x_Sx : (x:N)x<(S x).
+Axiom lt_S_compat : (x,y:N)(x<y)->(S x)<(S y).
+
+Axiom lt_eq_compat : (x1,x2,y1,y2:N)(x1=y1)->(x2=y2)->(x1<x2)->(y1<y2).
+Axiom lt_add_compat_l : (x,y,z:N)(x<y)->((x+z)<(y+z)).
+
+Hints Resolve eq_refl eq_trans add_sym add_eq_compat add_assoc_l add_x_0 
+	      S_eq_compat add_Sx_y S_0_1 lt_x_Sx lt_S_compat
+              lt_trans lt_anti_sym lt_eq_compat lt_add_compat_l : num.
+Hints Immediate eq_sym : num.
+  
+\ No newline at end of file