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Specification oset
enrich
   oseta
with
   

   
   
   functions  . .min : set → elem;
              . .butmin : set → set;
              . .max : set → elem;
              . .butmax : set → set;
   predicates  . < . : elem × set;
               . < . : set × elem;
   
   
   
   

   

   axioms Min-in :  ⊦ s ≠ ∅ → s.min ∈ s;
          used for: lf, kodkodaxstrong;
          Min-min :  ⊦ a ∈ s → ¬ a < s.min;
          used for: lf, kodkodaxstrong;
          Butmin :  ⊦ s ≠ ∅ → s.butmin = s -- s.min;
          used for: ls, kodkodaxstrong;
          Max-in :  ⊦ s ≠ ∅ → s.max ∈ s;
          used for: lf, kodkodaxstrong;
          Max-max :  ⊦ a ∈ s → ¬ s.max < a;
          used for: lf, kodkodaxstrong;
          Butmax :  ⊦ s ≠ ∅ → s.butmax = s -- s.max;
          used for: ls, kodkodaxstrong;
          Less :  ⊦ a < s ↔ (∀ b. b ∈ s → a < b);
          used for: ls;
          Greater :  ⊦ s < a ↔ (∀ b. b ∈ s → b < a);
          used for: ls;

   

   
end enrich