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Specification rtc
enrich
   nat
with
   functions 
       . ^* : ('a × 'a → bool) → 'a × 'a → bool;
       rtc : nat × ('a × 'a → bool) → 'a × 'a → bool;
   
   variables 
       pelem : 'a × 'a → bool;
       a : 'a;
       b : 'a;
       c : 'a;
       n : nat;
   
   
   axioms 
      rtc: pelem ^*(a, b) ↔ (∃ n. rtc(n, pelem)(a, b));
      
      rtc-base: rtc(0, pelem)(a, b) ↔ a = b;
      used for: ls;
      
      rtc-rec: rtc(n + 1, pelem)(a, b) ↔ (∃ c. pelem(a, c) ∧ rtc(n, pelem)(c, b));
      used for: ls;
   
   
end enrich