Specification olist-min-max

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enrich
   olist-sort, 
   gelem-min-max, 
   filter-count
with
   variables 
       x : list;
       a : elem;
   
   partial functions 
       min : list → elem with λ x. x ≠ [];
       max : list → elem with λ x. x ≠ [];
   
   
   axioms 
      min-base: min(a ') = a;
      used for: s, ls;
      
      min-rec: x ≠ [] → min(a ' + x) = (a < min(x) ⊃ a;min(x));
      
      max-base: max(a ') = a;
      used for: s, ls;
      
      max-rec: x ≠ [] → max(a ' + x) = (max(x) < a ⊃ a;max(x));
   
   
end enrich