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