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Specification infset-basic
generic specification
   

   
parameter
   elem

   using nat
target
   sorts set;
   constants  ∅ : set;
   functions  . ++ . : set × elem → set prio 9 left;
   predicates  . ∈ . : elem × set;
               . ⊆ . : set × set;
   
   variables  s : set;
              s0 : set;
              s1 : set;
              s2 : set;
   
   

   

   axioms 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;
          comment: sets which are potentially infinite (no generation principle).
          They are used exclusively here to model the ether
          (of course we could use a dynamic predicate for ether too).;

   

   
end generic specification