In short: The problem is that the jar package repeats the conflict!
At the beginning of this question I appeared a "self-righteous" answer, in the Android Private libraries directory will be packaged into the project executable, and not automatically compiled because the libs below the jar file is too large to cause, But obviously, when it's running, it's a direct error--class not found!
So obviously that's not the problem!
In fact, there is a android-support-v4.jar under the Libs directory. And if you have a project that introduces other libraries
And if there is android-support-v4.jar in this project, then the problem arises. The V4jar package under the Libs of the current project is duplicated with the V4jar package under the Libs of the included library project. At this time, the current project will not put any of the following Libs the jar into the auto-generated Android Private libraries directory, this directory will not be generated.
Solution: The current project in the Android-support-v4.jar to delete it! Then Clean,build. It's OK.
Why the jar file under the Libs folder is not automatically placed in the Android Private libraries directory