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 State of S, l being Nat
  holds DataPart s = DataPart(s +* Start-At(l,S))
proof
  let s be State of S;
  let l be Nat;
  thus DataPart s =  DataPart s +* {}
      .=  DataPart s +* DataPart Start-At(l,S) by Th20
      .= DataPart(s +* Start-At(l,S))by FUNCT_4:71;
end;
