IntelliJ IDEA 13 uses Java 1.5 despite setting to 1.7

Question

Despite specifying JDK 1.7 in all project settings (including in File -> Project Structure -> Project :: Project SDK), the following error is produced by

Answer 1

One more thing that could cause this is having incorrect version of the project.

In my case it was pointing to a non-existing project and for some reason IntelliJ downgraded version in settings to 1.5 and later when I fixed it, it was still interpreting target code version as 5 (despite setting it to 11).