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This was kind of straight forward. Use contract for the eliminateDuplicates method call and inline method for the report method.
IMPORTANT:
When loading the .proof file one needs to drag the \exists int n;(...) on the right side onto the \forall int i on the left side. Then auto-solve and the proof is complete.
(We couldn't save a new proof when working in a .proof file.)
Exception in thread "AWT-EventQueue-0" java.lang.NullPointerException
at de.uka.ilkd.key.gui.KeYFileChooser.showSaveDialog(KeYFileChooser.java:117)
at de.uka.ilkd.key.gui.WindowUserInterface.saveProof(WindowUserInterface.java:328)