Specification map-ops

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enrich
   map+set
with
   functions 
       . map ( . ) : Map × (Data → Data) → Map;
       . map ( . ) : Map × (Elem × Data → Data) → Map;
   
   variables 
       dataf : Data → Data;
       elemdataf : Elem × Data → Data;
       a : Elem;
   
   axioms 
      map-in: a ∈ st.map(dataf) ↔ a ∈ st;
      used for: s, ls;
      
      map-at: a ∈ st → st.map(dataf)(a) = dataf(st(a));
      used for: ls;
      
      mapi-in: a ∈ st.map(elemdataf) ↔ a ∈ st;
      used for: s, ls;
      
      mapi-at: a ∈ st → st.map(elemdataf)(a) = elemdataf(a, st(a));
      used for: ls;
   
   
end enrich