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, cf1 : ref → cell; 
      af0, 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