「~さえ~ば(なら)」は・・・が成り立つための必要最低限の条件を示す。


> 「~さえ~ば(なら)」は・・・が成り立つための必要最低限の条件を示す。

I do not know why the ため is used in the middle of this sentence. As far as I
know ため is used for 2 purposes: 1-原因 2-目的

成り立つ is modifying the ため, so does it mean that 成り立つ is the 原因 or 目的？




I find what your book provided a bit confusing. So, I looked up this
grammatical structure in one of my reference books. This is what I found:

**... さえ ... たら/ ... ば**

They define the semantics of this as:

> あるものごとが実現すればそれで十分で、ほかはちいさなことだ、必要ではない、問題ではない、という気持ちを表す。

Several examples are provided using subtle changes of the grammar:

  * あなたさえそばにいてくだされば、ほかにはなにもいりません。
  * 今度の試験で何がでるのかさえわかったらなあ

_Source: 日本語文型辞典_ I found this grammar dictionary very useful. It uses very
simple Japanese explanations and rather straight-forward examples. It
supplemented my other learning material very well.

I leave the translation of these example sentences for you to speculate on.

But, regarding the semantics, what was expressed was

> [This structure] expresses the feeling that if a certain occurrence should
> happen, that would be sufficient; anything else is a small matter, not
> necessary, not a problem.

* * *

So now let's return to your question,

> What is meant by ため in this phrase 成り立つための必要最低限の条件を示す?

ため is expressing purpose. In other words

> ...ための必要最低限

is saying

> _the absolute minimum necessary for ..._

