Android and iOS -- Build Once Run anywhere???

This piece talks about new releases from Adobe that allow certain kinds of Flash based apps to run in iOS: http://rww.to/mbrASk. Interesting in itself, but we were struck by this line:

the use of third-party development tools, which had previously prohibited the use of Adobe's Flash, Sun's Java and Microsoft Silverlight as well as its open source counterpart Mono, in creating apps for the iOS platform

Clearly Adobe want to position themselves this way, but what about Java? If someone came up with a set of common libraries, could you build java apps using a single code base for both platforms?