on/under/with the assumption

idiom

Definition of on/under/with the assumption

: as though one knows : in the belief We are operating on/under/with the assumption that the loan will be approved.

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“On/under/with the assumption.” The Merriam-Webster.com Dictionary, Merriam-Webster Inc., https://www.merriam-webster.com/dictionary/on%2Funder%2Fwith%20the%20assumption. Accessed 10 December 2019.

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