Specification list-getput

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enrich
   list-data
with
   variables 
       x : List;
       y : List;
       z : List;
       a : Elem;
       b : Elem;
       c : Elem;
       m : Nat;
       n : Nat;
   
   partial functions 
       . [ . ] : List × Nat → Elem with λ x, n. n < # x;
      comment: get is zero based;
       . [ . ] : List × Nat × Elem → List with λ x, n, a. n < # x;
      comment: put is zero based;
   
   
   axioms 
      get-zero: (a + x)[0] = a;
      used for: s, ls;
      
      get-succ: (a + x)[n + 1] = x[n];
      used for: s, ls;
      
      put-zero: (b + x)[0, a] = a + x;
      used for: s, ls;
      
      put-succ: (b + x)[n + 1, a] = b + x[n, a];
      used for: s, ls;
   
   
end enrich