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Specification store
generic specification
   

   
parameter
   elemdata

   using nat
target
   sorts store;
         elemdata;
   constants  ∅ : store;
   functions  . × . : elem × data → elemdata;
              . [ . ] : store × elem × data → store;
              . [ . ] : store × elem → data;
              # . : store → nat;
              . -- . : store × elem → store prio 9 left;
   predicates  . ∈ . : elem × store;
               . ∈ . : elemdata × store;
               . ⊆ . : store × store;
   
   variables  st : store;
              st0 : store;
              st1 : store;
              st2 : store;
              elemdatavar : elemdata;
   
   

   induction store generated by ∅, [ ];
             elemdata freely generated by ×;

   axioms Extension :  ⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a]);
          used for: ls, nokodkodax;
          In-empty :  ⊦ ¬ a ∈ ∅;
          used for: s, ls;
          In-insert :  ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st;
          used for: s, ls;
          At-same :  ⊦ st[a, d][a] = d;
          used for: s, ls, nokodkodax;
          At-other :  ⊦ a ≠ b → st[b, d][a] = st[a];
          used for: s, ls;
          In-store :  ⊦ a × d ∈ st ↔ a ∈ st ∧ st[a] = d;
          used for: s, ls, nokodkodax;
          Subset :  ⊦ st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a]);
          used for: ls;
          Size-empty :  ⊦ # ∅ = 0;
          used for: s, ls;
          Size-insert :  ⊦ ¬ a ∈ st → # st[a, d] = # st + 1;
          used for: s, ls;
          Del-in :  ⊦ a ∈ st -- b ↔ a ≠ b ∧ a ∈ st;
          used for: s, ls, nokodkodax;
          Del-at :  ⊦ a ≠ b → (st -- b)[a] = st[a];
          used for: s, ls, nokodkodax;

   

   
end generic specification