Specification maplet

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enrich heap-sep with
   functions 
       . => . : ref × obj → heap → bool prio 11;
       . =>_ : ref → heap → bool;
       . =>? : ref → heap → bool;
      _∃ . : (ref → heap → bool) → heap → bool;
      _∃ . : (ref × ref → heap → bool) → heap → bool;
      _∃ . : (obj → heap → bool) → heap → bool;
   variables 
      rP : ref → heap → bool; 
      rrP : ref × ref → heap → bool; 
      oP : obj → heap → bool; 
   
   axioms 
      ex1 :  ⊦ (_∃ rP)(H) ↔ (∃ r. rP(r)(H));
      used for : s, ls;
       
      ex2 :  ⊦ (_∃ rrP)(H) ↔ (∃ r0, r1. rrP(r0, r1)(H));
      used for : s, ls;
       
      ex3 :  ⊦ (_∃ oP)(H) ↔ (∃ o. oP(o)(H));
      used for : s, ls;
       
      maplet :  ⊦ (r => o)(H) ↔ ¬ ¬ (H = (∅ ++ r)[r, o] ∧ r ≠ null);
      used for : ls;
       
      mapex :  ⊦ r =>_ = _∃ λ o. r => o;
      used for : ls;
       
      mapornull :  ⊦ r =>? = ((r = null ⊃ emp; r =>_));
      used for : ls;
       
end enrich