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Specification array
enrich
   nat
with
   sorts array('a);
   functions 
       mkarray : nat → array('a);
       # . : array('a) → nat;
   
   variables 
       ar : array('a);
       m : nat;
       n : nat;
       a : 'a;
       b : 'a;
       c : 'a;
   
   partial functions 
       . [ . ] : array('a) × nat → 'a with λ ar, n. n < # ar;
       . [ . := . ] : array('a) × nat × 'a → array('a) with λ ar, n, a. n < # ar;
   
   
   induction 
      array('a) generated by mkarray, [ := ];
   
   axioms 
      Extension: ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]);
      used for: ls;
      
      Size-mkarray: # mkarray(n) = n;
      used for: s, ls;
      
      Size-put: # ar[n := a] = # ar;
      used for: s, ls;
      
      Put-same: m < # ar → (ar[m := a])[m] = a;
      used for: s, ls, lc;
      
      Put-other: m ≠ n → (ar[n := a])[m] = ar[m];
      used for: s, ls, lc;
   
   
end enrich