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;

theorem Th9:
  dom DataPart s = Data-Locations S
proof
  Data-Locations S c= dom s by Th8;
  hence thesis by RELAT_1:62;
end;
