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Specification rtc
enrich
   nat, 
   elem
with
   

   
   
   functions  . ^* : (elem × elem → bool) → elem × elem → bool;
              rtc : nat × (elem × elem → bool) → elem × elem → bool;
   
   
   variables  Pelem : elem × elem → bool;
   
   

   

   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