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Specification nat-prime
enrich
   nat-div
with
   

   
   
   functions  gcd : nat × nat → nat;
              dist : nat × nat → nat;
   predicates  prime : nat;
               . | . : nat × nat;
   
   
   
   

   

   axioms Prime :  ⊦ prime(n) ↔ 1 < n ∧ (∀ m. m | n → m = 1 ∨ m = n);
          used for: nokodkodax;
          Divides :  ⊦ m | n ↔ (∃ n0. m * n0 = n);
          used for: nokodkodax;
          gcd-zero :  ⊦ gcd(0, n) = n;
          gcd-c :  ⊦ gcd(m, n) = gcd(n, m);
          gcd-rec1 :  ⊦ n ≤ m → gcd(m, n) = gcd(m - n, n);
          dist-fst :  ⊦ m ≤ n → dist(m, n) = n - m;
          dist-snd :  ⊦ n < m → dist(m, n) = m - n;

   

   
end enrich