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Specification nat-even
enrich
   nat-div
with
   functions 
       max : Nat × Nat → Nat;
       min : Nat × Nat → Nat;
   
   predicates 
       even : Nat;
       odd : Nat;
   
   variables 
       m : Nat;
       n : Nat;
   
   
   axioms 
      Even-new: even((* n)) ↔ n % 2 = 0;
      used for: s, ls;
      
      Odd-new: odd((* n)) ↔ n % 2 ≠ 0;
      used for: s, ls;
      
      Max-left: m < n → max(m, n) = n;
      used for: s, ls, lc;
      
      Max-right: ¬ m < n → max(m, n) = m;
      used for: s, ls;
      
      Min-left: m < n → min(m, n) = m;
      used for: s, ls, lc;
      
      Min-right: ¬ m < n → min(m, n) = n;
      used for: s, ls;
   
   
end enrich