Specification maplet

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enrich
   heap-sep
with
   functions  . => . : ref × obj → heap → bool prio 11 right;
              . =>_ : 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;
              hP : heap → bool;
              h : heap;
              o : obj;
              r : ref;
   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