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Specification list-perm
enrich
   list-set
with
   

   
   
   functions  #oc : elem × list → nat;
   predicates  perm : list × list;
               . ⊆m . : list × list;
   
   
   
   

   

   axioms oc-e :  ⊦ #oc(a, []) = 0;
          used for: s, ls;
          oc-y :  ⊦ #oc(a, a ' + x) = #oc(a, x) + 1;
          used for: s, ls;
          oc-n :  ⊦ a ≠ b → #oc(a, b ' + x) = #oc(a, x);
          used for: s, ls, lc;
          msubset :  ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y));
          used for: ls;
          perm :  ⊦ perm(x, y) ↔ x ⊆m y ∧ y ⊆m x;
          used for: s, ls;

   

   
end enrich