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Specification array-perm
enrich
   array

with
   
   
   functions  #oc : elem × array × nat → nat;
   predicates  perm : array × array;
   
   

   

   axioms perm-def :  ⊦ perm(ar, ar0) ↔ # ar = # ar0 ∧ (∀ a. #oc(a, ar, # ar) = #oc(a, ar0, # ar0));
          numoc-base :  ⊦ #oc(a, ar, 0) = 0;
          numoc-rec :  ⊦ #oc(a, ar, n + 1) = #oc(a, ar, n) + (ar[n] = a ⊃ 1;0)

   

   
end enrich