Specification oelem-min-max

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enrich
   oelem
with
   functions 
       min : Elem × Elem → Elem;
       max : Elem × Elem → Elem;
   
   variables 
       a : Elem;
       b : Elem;
   
   axioms 
      Min-left: a < b → min(a, b) = a;
      used for: s, ls;
      
      Min-right: ¬ a < b → min(a, b) = b;
      used for: s, ls;
      
      Max-right: a < b → max(a, b) = b;
      used for: s, ls;
      
      Max-left: ¬ a < b → max(a, b) = a;
      used for: s, ls;
   
   theorems 
      min-def: min(a, b) = (a < b ⊃ a;b);
      used for: ls;
      
      max-def: max(a, b) = (a < b ⊃ b;a);
      used for: ls;
   
   
end enrich