Specification heap-fun

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enrich
   ex-maplet
with
   functions 
       mk : Set[Ref[A]] × (Ref[A] → A) → Heap[A];
   
   predicates 
       . [ . ] : (Heap[A] → Bool) × Set[Ref[A]] × (Ref[A] → A);
   
   variables 
       f : Ref[A] → A;
       r : Ref[A];
       rs : Set[Ref[A]];
       hP : Heap[A] → Bool;
       rhP : Ref[A] → Heap[A] → Bool;
       rrhP : Ref[A] × Ref[A] → Heap[A] → Bool;
       o : A;
       bv : Bool;
       oP : A → Heap[A] → Bool;
       h : Heap[A];
   
   
   axioms 
      in-mk: r ∈ mk(rs, f) ↔ r ∈ rs;
      used for: s, ls;
      
      at-mk: r ∈ rs → mk(rs, f)(r) = f(r);
      used for: s, ls, c, lc;
      
      apply: hP[rs, f] ↔ hP(mk(rs, f));
      used for: ls;
   
   
end enrich