Why this protected member is not visible in the subclass

I have a problem understanding protected members inheritance and visibility.

I know it is visible in the same package and subclasses.

But in the following code it is not visible in a subclass.

A.java

package a;

public class A {

    public static void main(String[] args) {

    }

    protected void run() {

    }
}

B.java

package b;

import a.A;

public class B extends A {
    public static void main(String[] args) {
        B b = new B();
        b.run(); // this works fine
    }
}

C.java

package b;
import a.A;

public class C extends A{ // it will not work also if extends B
    public static void main(String[] args) {
        B b = new B();
        b.run(); // this is the problem; not visible
    }
}

Why b.run() in the last class is invisible?

Solution

This is because class C can see A's protected methods from within its own inheritance tree. But it's not allowed to access A's protected methods for another class (B) from a different inheritance tree. C is not part of B's inheritance tree (by this, I mean that's it's not a parent of B), therefore the behavior is normal.

EDIT: Added documentation reference as requested

6.6.2.1. Access to a protected Member:

If the access is by a field access expression E.Id, or a method invocation expression E.Id(...), or a method reference expression E :: Id, where E is a Primary expression (§15.8), then the access is permitted if and only if the type of E is S or a subclass of S.

Applying the above to this case, because the variable b is not an instance of C or a subclass of C, access to the protected method b.run() is not allowed.

Also addressing Codebender's comment about the packages. Note that, if the C class would have been defined in the same package as the A class, where the protected run() method is defined, then the above rule wouldn't apply, and you would be able to access the method as shown in your code.