I. The first-instance court ascertained that the house lease contract executed between the Appellant and the Appellee on May 14, 1998 was invalid. This ruling is not law-based.
一、一审法院认定1998年5月14日上诉人与被上诉人签订的房屋租赁合同为无效合同，与法无据。

法院一审作出判决，认定他挪用公款不能退还的行为构成贪污罪。
The court convicted him in first instance and confirmed that his embezzlement of public funds without means to return them constituted a crime of corruption.

http://www.cn-teacher.com/yyjy/flyy/flyy1/200705/210310.html

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Note added at 23 mins (2008-06-18 04:33:23 GMT)
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The court of appeal is concerned that the judge at first instance has delivered judgment without proper arguments.
上诉法院担心，法官在一审时所作判决没有合适的论据

In 2000, China's courts tried or handled over 560,000 criminal cases at the first instance, in which more than 640,000 criminals were sentenced;
２０００年，全国法院共审理各类一审刑事案件５６万余件，判处罪犯６４万余人；

the court - [tried, judged, handled] - first instance - it can be phrased differently depending on grammar, context, etc, but these are the main components of translation

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Note added at 27 mins (2008-06-18 04:36:57 GMT)
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then for 认定, you can say "the courts judgment..., the court decided..., the court found....

i.e. Again the Court found no due process violation, because the prisoner could have sought redress through a tort action.
最高法院再次认定不存在违反正当程序的行为，因为该犯人可以通过侵权诉讼寻求补偿。

FYI

一审 has been asked before

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Note added at 1 hr (2008-06-18 05:35:45 GMT)
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but it was for a divorce case.