赞同jajil老师的解答。there be的非谓语形式有两种：一种是there to be，另一种是there being。

1. there to be可用作少数几个动词的宾语，常见的有like, hate, prefer, mean（打算；想要）, intend, want, expect, wish等等，因为这些动词之后常接不定式作宾语。例如：

I don't want there to be any misunderstanding. 我可不希望有任何误解。

We expect there to be more discussion about this. 我们期望能对此展开更多的讨论。

2. there being可用作主语，也常用在跟动名词的动词（deny, appreciate, mind, imagine, admit等）后作宾语。例如：

There being no money is a painful thing to him. 没有钱对他来说是很不好受的。

She denied there being misunderstanding between them. 她否认她们之间存在误会。

3. there being可用作介词宾语，但在介词for之后要用there to be。对照：

No one told him about there being a meeting that afternoon. 没人通知他那天下午有个会。

It's impossible for there to be a happier family. 不可能有比这个家庭更幸福的家庭了。

4.  there being还可构成独立主格结构，在句中作状语。例如：

There being no bus, we had to walk home. 由于没有公共汽车，我们只好走回家。

▲你的句子是there to be...作表语，是由第1条的句式演变而来。即：

He wanted there to be  progress in them. 他想要他们能有所进步。

→ What he wanted was there to be  progress in them. 他想要的是他们能有所进步。