Specification list-perm

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enrich
   list-set
with
   functions 
       #oc : 'a × list('a) → nat;
   
   predicates 
       perm : list('a) × list('a);
       . ⊆m . : list('a) × list('a);
   
   variables 
       x : list('a);
       y : list('a);
       z : list('a);
       a : 'a;
       b : 'a;
       c : 'a;
       m : nat;
       n : nat;
   
   
   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