| 单词 | valid proof | 
| 释义 | valid proof Those caught without valid proof of payment are subject to a fine. Retrieved from Wikipedia CC BY-SA 3.0  Because of soundness, we know that the user must really act honestly in order to be able to provide a valid proof. Retrieved from Wikipedia CC BY-SA 3.0  The theorems are those formulae that appear as the concluding judgment in a valid proof. Retrieved from Wikipedia CC BY-SA 3.0  An unrecorded deed may be valid proof of ownership between the parties, but may have no effect upon third-party claims until disclosed or recorded. Retrieved from Wikipedia CC BY-SA 3.0  The lender will require valid proof of financial hardship and other financial information when the student applies. Retrieved from Wikipedia CC BY-SA 3.0  | 
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