Specification min-of-Pnat

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enrich
   nat
with
   functions 
       min : (Nat → Bool) → Nat;
   
   variables 
       pnat : Nat → Bool;
   
   
   axioms 
      min-def: (∃ n. pnat(n)) → pnat(min(pnat));
      
      min-leq-def: pnat(n) → min(pnat) ≤ n;
   
   
end enrich