Specification iter-set

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enrich maplet , 
       set-union
 with
   functions 
       . ⊗_ . : (elem → heap → bool) × set → heap → bool prio 12;
       . ∧_ . : (elem → heap → bool) × set → heap → bool prio 11;
   variables 
      aP : elem → heap → bool; 
   
   axioms 
      Sep-emp :  ⊦ aP ⊗_ ∅ = emp;
      used for : s, ls;
       
      Sep-ins :  ⊦ ¬ a ∈ s → aP ⊗_ (s ++ a) = aP(a) * aP ⊗_ s;
      used for : s, ls;
       
      And-emp :  ⊦ aP ∧_ ∅ = true;
      used for : s, ls;
       
      And-ins :  ⊦ ¬ a ∈ s → aP ∧_ (s ++ a) = (aP(a) ∧ aP ∧_ s);
      used for : s, ls;
       
end enrich