reserve x,N for set,
        k for Nat;
reserve N for with_zero set;
reserve S for IC-Ins-separated non empty with_non-empty_values
     Mem-Struct over N;
reserve s for State of S;
reserve p for PartState of S;

theorem
 for S being IC-Ins-separated non empty with_non-empty_values
       Mem-Struct over N
 for s being State of S
  holds dom  s = {IC S} \/ dom DataPart s by Th2,Th24;
