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Specification nat-div
enrich
   nat-mult
with
   

   
   
   
   
   
   
   partial functions  . / . : nat × nat → nat prio 11 right with λ n, m. m ≠ 0;
                      . % . : nat × nat → nat prio 11 right with λ n, m. m ≠ 0;
   

   

   axioms Divdef :  ⊦ n ≠ 0 → m / n * n ≤ m ∧ m < (m / n)+1 * n;
          used for: nokodkodax;
          Moddef :  ⊦ n ≠ 0 → m = m / n * n + m % n;
          used for: nokodkodax;

   

   
end enrich