Specification intnat

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enrich
   int-div, 
   nat-div
with
   functions 
       i→n : Int → Nat;
       n→i : Nat → Int;
   
   variables 
       m : Nat;
       n : Nat;
       i : Int;
       j : Int;
   
   
   axioms 
      Nat2int-zero: n→i(0) = 0;
      used for: s, ls;
      
      Nat2int-succ: n→i(n +1) = n→i(n) +1;
      used for: s, ls;
      
      Int2nat-zero: i→n(0) = 0;
      used for: s, ls;
      
      Int2nat-pos: 0 < i → i→n(i) = i→n(i - 1) + 1;
      
      Int2nat-neg: i < 0 → i→n(i) = i→n(~ i);
   
   
end enrich