Methods, including geometric algebraic method, deductive database method and paradigmatic prove method have been widely applied in the geometric theorem prove field.
在几何定理机器证明方法中，常用的有几何代数方法、演绎数据库方法和例证法等方法。
It constructs full information items based on requirement to get a redundancy protocol firstly, and then USES theorem proven to prove the security of the designed protocol.
该方法首先根据协议规范构造全信息项及冗余协议，使用定理证明保证冗余协议的安全性。
So, instead of proving the divergence theorem, namely, the equality up there, I'm going to actually prove something easier.
我将要证明一些稍简单的结论，而不是证明散度定理，也就是写在这儿的等式，接下来证明点简单的东西。
下面来证明这个定理。
No? OK, so let's see, so how are we going to actually prove this theorem?
没有了吗？，来看看，到底应该怎么证明这个定理呢？
So, actually, that's kind of a not so obvious theorem to prove, but maybe intuitively, start by finding any surface.
实际上，这不是一个容易证明的定理，直觉上，先任取一曲面。
Well, that's the statement of the theorem we are trying to prove.
这就是我们试图证明的定理。
OK, so let's try to prove this theorem, at least this part of the theorem We're not going to prove that just yet.
好，我们来证明这个定理，或者说其中某部分,我们先不证明这部分。
OK, and actually that's how we prove the theorem.
实际上，这也是我们证明的思路。
And now there is a theorem which I will not prove, but it's very easy to prove, and that is called the parallel axis theorem.
这个公式，我不会再验证了，但它很容易证明，它称为，平行轴定理。
OK, so just to give you an example of what you can prove it this way, you can prove Newton's theorem, which says the following thing.
给一个用这个可以作证明的例子，可以去证明牛顿定律，也就是。。。
Yes. I have a yes. Let me explain to you quickly why Stokes is true. How do we prove a theorem like that?
来快速解释一下，为什么Stokes定理是对的，我们怎么来证明这样的一个定理呢？
So, I want to tell you how to prove Green's theorem because it's such a strange formula that where can it come from possibly?
下面证明格林公式，这么怪的公式，怎么得到的呢？
To "prove the theorem" means to show that the implication is a tautology.
“证明这个定理”就是要证明这个蕴涵式是一个重言式。
To prove the theorem we shall suppose that the graph G is drawn on a sphere as described above.
为了证明这个定理，我们假定这个圆G能按上述方式画在一个球面上。
It discusses carefully the basic concepts and inference rule of the resolution principle. According to the discussion, resolution method is used to prove a mathematical theorem through a example.
对归结原理的基本概念与推理规则进行了讨论，并在此基础上通过实例探讨了归结推理方法在数学定理证明中的应用。
But now it has also helped prove a new mathematical theorem as well.
但现在这个结果同时也帮助证明了一个新的数学定理。
After analyzing several theory models of inductive reasoning, we use the Bayes Theorem to prove the premise probability principle, and integrate this theory with human mental process.
在分析多个理论模型的基础上，采用贝叶斯定理证明了前提概率原则，并将此原则与人类心理过程相结合，将归纳推理分解为连续进行的三步过程。
This paper uses several methods of complex functions theorey to prove fundamental theorem of algebra by argument principle, maximum modulus principle and minimum modulus principle.
从复变函数理论出发，利用辐角原理、最大模原理、最小模原理给出代数学基本定理的几种新的证明方法。
And we learned how to prove the Pythagorean Theorem in Euclidean geometry, starting with the various axioms in Euclidean geometry, ba, ba-ba, ba-ba, ba-ba, ba bum.
我们都学习过，欧几里得几何中对勾股定理的证明方法，从繁杂的欧氏几何的公理开始，邦，邦邦，邦邦，邦邦。
We prove the relativistic virial theorem, which gives simple criteria for the absence of embedded eigenvalues in certain regions of the continuous spectrum.
我们证明相对论维里定理，这定理对于连续谱空间里本征值的缺乏给出了简单的标准。
This article is to introduce separable proposition and separable proposition theorem, then to prove theorems in real number field by using separable proposition in a union form.
引入了可分命题和可分命题定理，利用该定理统一证明数学分析中的定理，极大简化了这些定理的证明过程。
This paper gives the new method to prove the cauchy mean value theorem which also may be deduced from the Lagrange mean value theorem.
给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。
In chapter two, we prove a nonempty intersection theorem in L-convex space by using a continuous selection theorem. As applications, some minimax inequalities are obtained.
在第二章中，我们运用一个连续选择定理证明了L -凸空间中的一个非空交定理。作为应用，我们得到了一些极大极小不等式。
Moreover, this method is conveniently used to prove the theorem for finite rotations of a rigid body, and to compose the finite rotations of a rigid body.
并用此法方便地证明了刚体的有限转动定理，进行了刚体有限转动的合成。
By using the fixed point theorem, we prove some new existence theorems of the solution for this class of nonlinear projection equations in Hilbert Spaces.
利用不动点定理，我们得到了关于这类非线性投影方程解的一些新的存在性定理。
In 1985, prove Theorem 1.1 from the point of Brown Motion. This paper USES the method of establishing the convex envelope, giving a proof in Partial Differential Equation.
在1985年从布朗运动的角度证明了定理1.1，本文利用构造凸包络的方法，给出了该定理偏微分上的证明。
Specifically, Lyapunov techniques are fused with LaSalle's Invariance Theorem to prove that the constructed nonlinear controllers achieve asymptotic regulation of the crane system.
本文通过将李亚普诺夫方法与拉塞尔不变性原理相结合，证明了所设计的控制算法能实现吊车系统的渐近镇定。
Specifically, Lyapunov techniques are fused with LaSalle's Invariance Theorem to prove that the constructed nonlinear controllers achieve asymptotic regulation of the crane system.
本文通过将李亚普诺夫方法与拉塞尔不变性原理相结合，证明了所设计的控制算法能实现吊车系统的渐近镇定。
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