What he said proved to be true.

to be true 是不定式作表语。

书上说这句话中 to be 可以省略，那么是不是可以理解为：

What he said proved true.

这句话中是使用形容词 true 作表语了呢？或者说其实没有什么语法现象，只是省略了而已。

解答如下：

以上prove是作系动词用法，意思“证明是/结果是/事实说明，当作系动词用法可以归纳一下几个结构

A: prove作为系动词用法几种结构归纳

(1)prove +（不定式to be） +n./adj.

As time went on, Einstein's theory proved to be correct.

随着时间的推移,爱因斯坦的理论证明是正确的. 

This has afterwards proved to be the correct explanation.  

后来证明这是正确的解释。

She may prove to be the most suitable person for the job.

结果她可能是最适合干这项工作的人.

The report proved to be true.  

这报告证明属实。

The new typist proved to be useless.  

那位新打字员终于被发现是无用的

(2)prove+形容词

The handbook proved most useful.

这本手册证明很有用. 

The medicine proved satisfactory.

结果证明这药疗效令人满意. 

The machine proved highly valuable in heart surgery.   
这种机器做心脏手术证明是非常有价值的。

Her rash marriage proved unhappy.   
她轻率结婚,很不幸福。

His first attempt proved successful.   
他的第一次尝试证明是成功的。

These methods have proved quite effective.   
这些办法证明是很有成效的。

Isotopes also prove helpful in other conditions.   
事实证明,在其他情况下,同位素也很有用处。

As it happened, my advice proved wrong.   
当此事发生时,我的意见证明是错误的。

(3)prove +名词

She proved a very strict teacher.

结果证明她是一位非常严格的老师. 

 His efforts, however, proved a failure.

但他的努力结果都失败了.

Mary proved a qualified teacher.   
玛丽被证实是个称职的教师。

She proved a good wife.   
她证明是一个好妻子。

He proved a reliable friend of the Chinese people.   
事实证明他是中国人民的可靠朋友。

I imagined it would prove an easy task.   
我想它将证明是件容易的工作。

This has proved an effective preventive.   
这种药证明是很有效的预防剂。

The concert proved a great success.   
音乐会取得了巨大成功。

His efforts, however, proved a failure.   
但他的努力结果都失败了。

He proved a coward.  

他证明是个懦夫。

(4)prove+介词短语或副词 

Perhaps this book will prove of some use to you in your studies.

也许这本书会对你的研究有用处. 

The power station was completed and proved up to standard.

这座发电站建成了,证明质量符合标准.

B:prove 作为行为动词用法归纳为以下结构 

(1)prove+名词/代词

He has proved his courage in the battle.

他已在作战中证明了他的勇气.

This further proved the strength of our economy.

这进一步证明了我们的经济实力.

Can you prove that?

你能证实那一点吗?

Who can prove it?   
谁能证实这一点呢?

This further proved the strength of our economy .   
这进一步证明了我国经济的实力。

Facts will prove my sincerity.   
事实将会证明我是真心实意的。

(2)prove+直接宾语(sth.)+to+间接宾语(sb.)

The difficulty was how he could prove his ideas to other scientists

困难在于他怎样向其他科学家证实他的想法.

Can you prove your theory to us?

你能向我们证实你的理论吗? 

(3)prove+宾语+宾语补足语

A:形容词作宾语补足语

They proved themselves wise and brave.

他们证实自己机智、勇敢.

Facts have proved these worries groundless.

事实证明,这些忧虑是没有理由的.

B:名词作宾语补足语 

She proved herself an able secretary

她证实自己是个能干的秘书.

He has proved himself a success.

他已证明了自己是个成功者.

C:动词不定式作宾语补足语 

 All this proved him to be an honest man.

这一切都证明他是一个诚实的人.

The experiment proved his theory to be important to our research.

实验证明他的理论对我们的研究是重要的.

She proved him to be the thief.   
她证明他就是那小偷。

I'll prove it to be erroneous.   
我将证明它是错误的。

He has proved himself to be worthy of revering.   
他证明自己值得尊敬。

(4)prove+宾语从句 

They proved that he was guilty.  

他们证明他有罪。

How can you prove that you are right?  

你如何能证明你是正确的呢?

He has proved that his hypothesis is correct.  

他已经证明自己的假设是正确的。

Galileo proved that the earth and all other planets move around the sun.

伽利略证实地球和所有其它的行星都是绕太阳运转的.

But Einstein was able to prove that light coming from the stars was bent as it passed the sun.

然而爱因斯坦却能证明从恒星来的光线当其经过太阳时变弯曲了.

Can you prove where you were on May 10th?

你能证实五月十日你在什么地方吗?