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Specification list-perm
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