Specification linked-list-aux

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enrich
   cell-heap-aux
, 
   list
with
   

   
   
   functions  ls : ref × list → heap → bool;
              lst : ref → heap → bool;
              _∃ . : (list → heap → bool) → heap → bool;
   
   
   variables  cf0 : ref → cell;
              cf1 : ref → cell;
              af0 : ref → aux;
              af1 : ref → aux;
              xv : list → heap → bool;
   
   

   

   axioms ex-lst :  ⊦ (_∃ xv)(mk(rs, cf)) ↔ (∃ x. xv(x)(mk(rs, cf)));
          ls-base :  ⊦ ls(r, []) = (emp ∧ ⌜r = null⌝ );
          used for: s, ls;
          ls-rec :  ⊦ ls(r, a ' + x) = _∃(λ r0. r => a × r0 * ls(r0, x));
          used for: s, ls;
          lst-def :  ⊦ lst(r) = (r = null ⊃ ls(r, []);_∃(λ x. ls(r, x)));
          used for: ls;

   

   
end enrich