Specification dlinked-maplist

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enrich
   node, 
   refmap-separation, 
   list
with
   functions 
       dll : Ref[Node[A]] × List[A] → Map[Ref[Node[A]], Node[A]] → Bool;
       dll : Ref[Node[A]] × Ref[Node[A]] × List[A] → Map[Ref[Node[A]], Node[A]] → Bool;
   
   variables 
       r : Ref[Node[A]];
       x : List[A];
       y : List[A];
       z : List[A];
       a : A;
       b : A;
       c : A;
       h : Map[Ref[Node[A]], Node[A]];
       hP : Map[Ref[Node[A]], Node[A]] → Bool;
       nd : Node[A];
   
   
   axioms 
      dll: dll(r, x) = dll(r, null, x);
      used for: s, ls;
      
      dll-base: dll(r, r0, []) = (emp ∧ ⌜r = null⌝ );
      used for: s, ls;
      
      dll-rec: dll(r, r0, a ' + x) = _∃(λ r1. r => mknode(r0, a, r1) * dll(r1, r, x));
      used for: s, ls;
   
   
end enrich