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Secondly, by using of the medium axiomatic set theory, a natural number system in MS is constructed, and it is proved that five axioms of Peano′s natural number system are theorems is MS.

其次，利用中介公理集合论MS的相关理论，构造了MS中的自然数系统，证明了Peano5条公理为MS中的定理。

It has proved that well sets completely satisfy all axioms of ZFC -(the classical system of axiomatic set theory ZFC without the regular axiom).

在中介公理集合论系统中重新定义了良集的概念，讨论了它的性质。

In the main body of the text,results that are easily proved from these axioms are used without comment.

在本书的正文中，从这些公理出发所方便得出的结论在使用时，无须标注出来。

The best laid schemes o'mice an' men gang aft a-gley...' Since Rab Burns, the great Ayrshire bard wrote this, long ago, nothing has proved him wrong.

"再周详的方案也会出错"，很久以前，苏格兰埃尔郡的吟游诗人罗宾彭斯写道，他并没有说错。

It has also been proved that azotobacter CN-2 has a property of secreting hormone material similar to IAA.

固氮菌CN-2还具有分泌吲哚乙酸类植物激素的功能。

He found that the red pigment proved to be iron oxide, hematite; a yellow consisted of clay containing iron or yellow ochre; a blue color was a finely powdered glass; and a pale blue was a copper carbonate, probably azurite; green were malachite; black was charcoal or boneblack; gray, a limestone mixed with charcoal; and a quantity of pigment remaining in a paint pot used in the decoration, contained a mixture of hematite with limestone and clay.

他发现红颜料是铁的氧化物赤铁矿；黄色颜料由含有铁或黄赭色粘土组成；蓝颜色为细微的玻璃粉；而普蓝就是碳酸铜，或许是蓝铜矿；绿颜料为孔雀石；黑色为木炭或骨黑；灰色，石灰石混合木炭而成；而一些颜料残留在用于彩绘装饰的颜料瓶里，含有赤铁矿与石灰石及粘土的混合物。

Back 'down; US back 'off give up a claim to sth; yield 放弃对某事物的要求;屈服: He proved that he was right and his critics had to back down.

他证明了他是正确的，而那些非难他的人不得不收起他们那一套。

The premise of plane background in the global motion estimation and compensation is proved from the theoretical and instance analysis.

一种是在给定采样帧率的条件下，以运动分析为基础，利用运动场总体能量和运动补偿后的残差能量来综合度量运动变化信息，建立了基于运动变化信息熵最大化的视频序列时域亚采样技术。

The backset current of the transferred agricultural labor force, and the phenomena of the "pleasant worker neglect" all proved this fact.

转移农村劳动力的回流、"民工荒"现象都佐证了这个事实。

But we should continue to enforce those reform measures that have proved effective and should not backtrack.

但是，已经从各方面证明行之有效的改革措施要继续实行，不能走回头路。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。