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CopyFileEx('A.txt'#0'B.txt'#0'C.txt', 'A.txt.bak'#0'B.txt.bak'#0'C.txt.bak', true);                    

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Procedure TForm1.CopyFileWithProgressBar(Source, Destination : string);
var
 FromF, ToF : file of byte;
 Buffer : array[0..4096] of char;
 NumRead : integer;
 FileLength : longint;
begin
  AssignFile(FromF,Source);
  reset(FromF);
  AssignFile(ToF,Destination);
  rewrite(ToF);
  FileLength:=FileSize(FromF);
  With Progressbar1 do
 begin
  Min := 0;
  Max := FileLength;
  while FileLength > 0 do
  begin
   BlockRead(FromF,Buffer[0],SizeOf(Buffer),NumRead);
   FileLength := FileLength - NumRead;
   BlockWrite(ToF,Buffer[0],NumRead);
   Position := Position + NumRead;
  end;
  CloseFile(FromF);
  CloseFile(ToF);
 end;
end;                    

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Procedure TForm1.CopyFileWithProgressBar(SourceFiles:TStrings, DestinationFolder : string);                    

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function PProgressRoutine(TotalFileSize,
                            TotalBytesTransferred,
                            StreamSize,
                            StreamBytesTransferred: LARGE_INTEGER;
                            dwStreamNumber,
                            dwCallbackReason: DWORD;
                            hSourceFile,
                            hDestinationFile: THandle;
                            lpData: Pointer): DWORD; stdcall;
begin
  if dwCallbackReason = CALLBACK_STREAM_SWITCH then
    TProgressBar(lpData).max := TotalFileSize.QuadPart;

  TProgressBar(lpData).Position := TotalBytesTransferred.QuadPart;
  Application.ProcessMessages;
  Result := PROGRESS_CONTINUE;
end;

procedure ListCopyProgress(const Files: TStrings; const aDestDir: string;
                           TotalProgressBar, CurrentProgressBar: TProgressBar);
var
  x, y : integer;
  S: string;
begin
  FCancelled := False;
  x:=Files.Count;
  TotalProgressBar.Min:=0;
  TotalProgressBar.Max:=x;
  S:=ExcludeTrailingPathDelimiter(aDestDir) + '\';
  for y:=0 to x-1 do
  begin
    CopyFileEx(PChar(Files[y]), PChar(S + ExtractFileName(Files[y])),
    @PProgressRoutine, CurrentProgressBar, @FCancelled, 0);
    
    TotalProgressBar.Position:=y+1;
  end;
end;