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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: even(n) ↔ (∃ m. m + m = n);
      
      Odd: odd(n) ↔ ¬ even(n);
      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