If we have a hash function $h(x)$ and then a hash function $H(X) = h(h(X_0) || h(X_1))$ where $X_0$ is the first half of $X$, $X_1$ is the second half of $X$ and $||$ is concatenation. Then assuming we can easily find a collision for $H$, then it would be easy to find a collision for $h$ as well - Therefore finding a collision for $H$ is as hard as finding one for $h$.
Why is this? I can to some extent understand why that might be the case, but I can't logically connect the dots. Can anyone help me with some logic or math behind it or link to some resources where it is explained. I have tried google, but without the precise correct terminology I'm having a hard time finding the right pages.