generic specification
   parameter elem
   using nat
target
   sorts set;
   constants 
       ∅ : set;
   
   functions 
       . ++ . : set × elem → set prio 9 left;
       χ : set → elem → bool;
       { . } : (elem → bool) → set;
   
   predicates 
       . ∈ . : elem × set;
       . ⊆ . : set × set;
   
   variables 
       s : set;
       a : elem;
       b : elem;
       f : elem → bool;
   
   
   induction 
      set generated by { };
   
   axioms 
      characteristic-function: χ(s)(a) ↔ a ∈ s;
      used for: s, ls;
      
      construct-set: a ∈ {f}  ↔ f(a);
      used for: s, ls;
      
      Extension: s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2);
      used for: ls;
      
      In-empty: ¬ a ∈ ∅;
      used for: s, ls;
      
      In-insert: a ∈ s ++ b ↔ a = b ∨ a ∈ s;
      used for: s, ls;
      
      Subset: s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2);
      used for: ls;
   
   
end generic specification