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;

theorem
  for S being Mem-Struct over N, p being data-only PartState of S
   holds DataPart p = p
proof
  let S be Mem-Struct over N, p be data-only PartState of S;
     dom p c= Data-Locations S by Th6;
    hence thesis by RELAT_1:68;
end;
