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repose on (someone or something)
1. To lie flat and at full length atop something. The patient reposed on the therapist's sofa, recounting the trauma of his childhood.
2. To be based on, exist in, or take support from something. For me, faith must repose on reason, logic, and evidence. Your belief reposes on a fantasy you've concocted in your mind. The dictatorship's power reposed on the fear of its citizens.
3. To impart or place something in some person, group, thing, action, or concept. In this usage, a noun or pronoun is used between "repose" and "on." Many reposed their hopes for a better on the new candidate, but found themselves underwhelmed once he actually took office. We found out long ago that we can no longer repose trust on the government.
repose (up)on something
to lie on something. (Upon is formal and less commonly used than on.) I will repose upon these cushions until my bathwater has been drawn. Dawn reposed on the sofa for over an hour.