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Specification list-set
enrich
   list-del
with
   

   
   
   functions  . ∪ . : list × list → list;
              . \ . : list × list → list;
             comment: x \ y : remove from x all elements that are in y;
              filter : list × list → list;
             comment: filter(x,y) : remove from x all elements that are not in y.;
   predicates  . ⊆ . : list × list;
   
   
   
   

   

   axioms subset :  ⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y);
          used for: ls;
          union :  ⊦ x ∪ y = rmdup(x + y);
          used for: nokodkodax;
          diff-e :  ⊦ [] \ y = [];
          used for: s, ls;
          diff-y :  ⊦ a ∈ y → (a ' + x) \ y = x \ y;
          used for: s, ls, lc;
          diff-n :  ⊦ ¬ a ∈ y → (a ' + x) \ y = a + (x \ y);
          used for: s, ls;
          filt-e :  ⊦ filter([], y) = [];
          used for: s, ls;
          filt-y :  ⊦ a ∈ y → filter(a ' + x, y) = a ' + filter(x, y);
          used for: s, ls, lc;
          filt-n :  ⊦ ¬ a ∈ y → filter(a ' + x, y) = filter(x, y);
          used for: s, ls;

   

   
end enrich