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

Please check your project/module language levels (Project Structure | Project; Project Structure | Modules | module-name | Sources). You might also want to take a look at Settings | Compiler | Java Compiler | Per-module bytecode version.

Set also this:

File -> Project Structure -> Modules :: Sources (next to Paths and Dependencies) and that has a "Language level" option which also needs to be set correctly.