to be based
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to be based on
To be based on something, be founded on something, or have something as a foundation. Used for facts, stories, principles, or assumptions.
Der Film beruht auf einer wahren Geschichte.
The film is based on a true story.
'Beruhen' (to be based) is an inseparable verb made up of the prefix 'be-' and the verb 'ruhen' (to rest). The meaning 'to be based on' comes from the idea that one thing 'rests' on another.
Die Statue ruht auf einem massiven Steinsockel.
The statue rests on a massive stone base.
The verb 'beruhen' (to be based) is always used with the preposition 'auf' and the dative. A connection with another case or another preposition is not correct.
Sein Erfolg beruht auf harter Arbeit und ein wenig Glück.
His success is based on hard work and a little luck.
The idiom 'etwas auf sich beruhen lassen' (to let something rest) has a fixed structure. 'Etwas' (something) is the accusative object of the verb 'lassen' (to let). It means deliberately not discussing a topic any further.
Wir waren uns uneinig, aber wir haben es dann auf sich beruhen lassen.
We disagreed, but then we let it rest.
to lock / to complete
'abschließen' and 'etwas auf sich beruhen lassen' (to let something rest) can both mean that you stop dealing with a matter. 'abschließen' often sounds more final: you finish a project or topic, or you internally move on from a difficult experience. 'etwas auf sich beruhen lassen' is used more when you do not pursue an argument, question, or problem any further. It does not necessarily mean that everything has really been processed. It means more: you leave it at that now.
Wegen der langen Diskussion lassen wir das Thema heute auf sich beruhen.
Because of the long discussion, we will let the topic rest for today.
Nach der letzten Besprechung hat das Team das Projekt endlich abgeschlossen.
After the final meeting, the team finally completed the project.