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Specification array
generic specification
   

   
parameter
   elem

   using nat
target
   sorts array;
   
   functions  mkarray : nat → array;
              . [ . ] : array × nat → elem;
              . [ . ] : array × nat × elem → array;
              # . : array → nat;
   
   
   variables  ar : array;
              ar0 : array;
              ar1 : array;
              ar2 : array;
   
   

   induction array 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 generic specification