enrich
   list-del
with
   functions 
       . ∪ . : List[A] × List[A] → List[A];
       . \ . : List[A] × List[A] → List[A];
      comment: x \ y : remove from x all elements that are in y;
       . intersect . : List[A] × List[A] → List[A];
      comment: filter(x,y) : remove from x all elements that are not in y.;
   
   predicates 
       . ⊆ . : List[A] × List[A];
   
   variables 
       x : List[A];
       y : List[A];
       z : List[A];
       a : A;
       b : A;
       c : A;
       m : Nat;
       n : Nat;
   
   axioms 
      subset: x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y);
      used for: ls;
      
      union: x ∪ y = (x + y).distinct;
      
      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;
      
      inters-e: [] intersect y = [];
      used for: s, ls;
      
      inters-y: a ∈ y → (a ' + x) intersect y = a ' + (x intersect y);
      used for: s, ls, lc;
      
      inters-n: ¬ a ∈ y → (a ' + x) intersect y = x intersect y;
      used for: s, ls;
   
   
end enrich