Eclipse Web-App Deployment with Tomcat: Providing multiple projects' dependencies?

Well, I've found the answer on my own meanwhile.

For those reading this in the future I will explain step by step, using the semantics I introduced in my original message:

First, open the properties page of your core project and navigate to the 'Libraries' tab of the 'Java Build Path' settings:

Make sure to add your class library a.jar, your core project depends on, via 'Add JARs...'. Then, go ahead to the 'Order and Export' tab and activate the just added a.jar for exporting.

Then go to the 'Deployment Assembly' settings and also add a.jar here by first clicking on 'Add...', then on 'Java Build Path Entries' and finally selecting a.jar. Make sure to enter '../' as the deploy path for a.jar:

Now you are done with your core project. Now open the 'Projects' page of the 'Java Build Path' settings for your web project and add your core project by clicking on 'Add...':

Finally, navigate to the 'Deployment Assembly' settings page, press 'Add...', then take 'Project' and select your core project on the next screen:

You're done. No need to add your core dependencies to your web project.