Definition of rest with phrasal verb from the Oxford Advanced Learner's Dictionary

 

rest with

 phrasal verb
phrasal verb
 
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Phrasal Verbs

rest with somebody (to do something)

 
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(formal) if it rests with somebody to do something, it is their responsibility to do it It rests with management to justify their actions. The final decision rests with the doctors.
See the Oxford Advanced American Dictionary entry: rest with