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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