Specification characteristic

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enrich
   infset-union
with
   

   
   
   functions  χ : set → elem → bool;
              { . } : (elem → bool) → set;
   
   
   variables  f : elem → bool;
   
   

   

   axioms characteristic-function :  ⊦ χ(s)(a) ↔ a ∈ s;
          used for: s, ls;
          construct-set :  ⊦ a ∈ {f}  ↔ f(a);
          used for: s, ls;

   

   
end enrich