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Specification olist
specification
   

   

   

   using actualize
            list-perm
         with
            gelem
         
            
         by morphism
            
         end actualize

   

   

   

   

   
   
   functions  ins≤ : elem × list → list;
              merge : list × list → list;
   predicates  ordered≤ : list;
               ordered< : list;
   
   
   
   

   

   axioms le-e :  ⊦ ordered≤([]);
          used for: s, ls, nokodkodax;
          le-o :  ⊦ ordered≤(a ');
          used for: s, ls, nokodkodax;
          le-r :  ⊦ ordered≤(a ' + b ' + x) ↔ ¬ b < a ∧ ordered≤(b + x);
          used for: s, ls, nokodkodax;
          ls-e :  ⊦ ordered<([]);
          used for: s, ls, nokodkodax;
          ls-o :  ⊦ ordered<(a ');
          used for: s, ls, nokodkodax;
          ls-r :  ⊦ ordered<(a ' + b ' + x) ↔ a < b ∧ ordered<(b + x);
          used for: s, ls, nokodkodax;
          ins-e :  ⊦ ins≤(a, []) = a ';
          used for: s, ls;
          ins-y :  ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;
          used for: s, ls;
          ins-n :  ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);
          used for: s, ls, lc;
          merge-empty :  ⊦ merge([], x) = x;
          used for: s, ls;
          merge-rec :  ⊦ merge(a ' + x0, x) = ins≤(a, merge(x0, x));
          used for: s, ls;

   

   
end specification