论证的英文：
prove a point
expound on
proof
demonstrate or prove

参考例句：

A substantial argument
重要的论证

My argument follows the rules of logical induction.
我是遵循逻辑归纳的法则进行论证的。

She was not really convinced by this line of reasoning.
这样的分析论证实际上并没有让她信服。

Her speech argued the case against atomic weapons very effectively.
她的发言就反对原子武器问题进行了十分有力的论证。

Any attempt to give a rational proof of the mysteries of religion really detracts from faith.
任何想合理论证宗教奥秘的做法，会使信念降低的。

Reading makes a full man, meditation a profound man, discourse a clear man.
博览群书使人完美无瑕，冥思苦想让人深刻精邃，论证阐述让人头脑清晰。

The engineers worked out the Math and designed a system of nylon ropes and pulleys.
工程师们从数学上进行了论证，并设计出一个由尼龙绳子和滑轮构成的工作系统。

The content of his argument was very weak.
他的论证非常不充分。

a rambling argument that lacked any consistency.
杂乱且不连贯的论证

Some of his arguments are illogical.
他的一些论证是不合逻辑的。

prove是什么意思：
v. 证明，证实；显示；证明是

Fire proves gold; adversity proves man
烈火见真金,逆境出好汉

The rumor proved true.
这谣传结果是真的。

They proved themselves talented and capable.
他们证明自己很有天赋和能力。

point是什么意思：
n. 点；标点；要点；尖端；得分
v. 削尖；指向；加标点于；表明

That is not the point in question.
那不是要考虑的要点。

orientation point
方位点

A score made on a try for a point or points after a touchdown.
触地得分在触地后再次发球所得的一分或几分

expound是什么意思：
v. 解释，详细说明

The teacher expounded a profound truth in common language.
老师用通俗的语言说明深刻的道理。

Never has a text been expounded with more complexity.
从来没有人能把一段经文讲解得这么玄妙深奥。

The speaker has an hour to expound his views to the public.
讲演者有1小时时间向公众阐明他的观点。