Specification list-dup

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enrich
   list
with
   

   
   
   functions  . ++ . : list × elem → list prio 9 left;
              rmdup : list → list;
             comment: removes from the beginning, i.e. the last occurrence of an
                                     element remains in the list.;
   predicates  dups : list;
               disj : list × list;
   
   
   
   

   

   axioms rmdup-e :  ⊦ rmdup([]) = [];
          used for: s, ls;
          rmdup-y :  ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);
          used for: s, ls;
          rmdup-n :  ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);
          used for: s, ls;
          adjoin-in :  ⊦ a ∈ x → x ++ a = x;
          used for: s, ls, lc;
          adjoin-notin :  ⊦ ¬ a ∈ x → x ++ a = a + x;
          used for: s, ls;
          dups :  ⊦ dups(x) ↔ (∃ a, x0, y, z. x = x0 + (a + (y + (a + z))));
          used for: nokodkodax;
          disjoint :  ⊦ disj(x, y) ↔ (∀ a. ¬(a ∈ x ∧ a ∈ y));

   

   
end enrich