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As it happens, the Document Viewer app in Google Galaxy Nexus phones is a read-only version of ThinkFree Office Mobile. Since this is a pre-packaged app, you cannot reinstall it from the Play Store once you uninstalled it. For that you've to back it up first. On a rooted phone you'll find the app in /system/app/Thinkfree.apk and to back it up you simply have to make a copy of the apk.

There's something interesting about this app though: the Document Viewer's version is 4.1.111031 on my Nexus. In the Play Store the read-only ThinkFree Office Mobile Viewer has a version number of 2.0.120220 (released on 20th Feb 2012) and is not compatible with Android 4.*. The ThinkFree Office Mobile app (the full version that can read and write office files) has no specific version number, they say it "varies with device". But according to online forums it's current version number for ICS is 4.1.*. So it'd seem that the development of the viewer and the full version app was split at some point: the viewer is only compatible with older Android versions, while the full version app was upgraded to be compatible with ICS. And most probably the Nexus got the full version, but handicapped to allow only reading of office files.