Why does estimation error increase with $|H|$ and decrease with $m$ in PAC learning? Why does estimation error increase with $|H|$ and decrease with $m$ in PAC learning?

I came across this statement in the section 5.2 of the book "understanding machine learning: from theory to algorithms". You just search "increases (logarithmically)" in your browser and then you can find the sentence.

I just can't understand the statement. And there is no proof in the book either. What I would like to do is prove that estimation error $\epsilon_{est}$ increase (logarithmically) with || and decrease with . Hope you can help me out. A rigorous proof can't be better!
Definitely, you can find the proof in different resources (for example, in these notes or in the paper that originally proposed PAC learnability, A Theory of the Learnable). However, the intuition behind your question is when the size of the hypothesis increases, if you do not change anything, you can't see more part of the space. Hence, the estimation error will increase. Moreover, when you increase the number of samples, you have more chance to see more part of the hypothesis space, hence, the estimation error decrease.
Also, you can see some lemma about the relation of the PAC learnability and other similar concepts in the Wikipedia article Probably approximately correct learning:

Under some regularity conditions these three conditions are equivalent:

The concept class $C$ is PAC learnable.
The VC dimension of $C$ is finite.
$C$ is a uniform Glivenko-Cantelli class.