- 以资鼓励 yǐzīgǔlì as an encouragementto provide as a means of encouragement; used in formal contexts like certificates or awards to indicate that a prize is given to encourage the recipient
- 以资证明 yǐzīzhèngmíng serving as proofformal expression used in legal or official documents to mean "in witness whereof" or "to serve as proof or evidence"