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Specification fsarray
generic specification
   parameter elem
   using nat
target
   sorts FSArray;
   constants 
       size : Nat;
       mkarray : FSArray;
   
   functions 
       # . : FSArray → Nat;
   
   variables 
       ar : FSArray;
       m : Nat;
       n : Nat;
       a : Elem;
   
   partial functions 
       . ( . ) : FSArray × Nat → Elem with λ ar, n. n < # ar;
       . ( . := . ) : FSArray × Nat × Elem → FSArray with λ ar, n, a. n < # ar;
   
   induction 
      FSArray generated by mkarray,  . (. := .) ;
   
   axioms 
      Extension: ar1 = ar2 ↔ (∀ n. n < size → ar1(n) = ar2(n));
      used for: ls;
      
      Size-array: # ar = size;
      used for: s, ls;
      
      Put-same: m < size → 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