I'm reading through the [RMIT course notes on state space search](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/).
Consider a state space $S$, a set of nodes in which we look for an element having a certain property.
A [heuristic function](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/07ImprovedMethods/07bHeurFunctions/) $h:S\to\mathbb{R}$ measures how promising a node is.

$h_2$ is said to *dominate* (or to be more informed than) $h_1$ if $h_2(n) \ge h_1(n)$ for every node $n$. How does this definition imply that using $h_2$ will lead to expanding fewer nodes? - not only fewer but subset of the others.

In Luger '02 I found the explanation:
>This can be verified by assuming the opposite (that there is at least one state expanded by $h_2$ and not by $h_1$). But since $h_2$ is more informed than $h_1$, for all $n$, $h_2(n) \le h_1(n)$, and both are bounded above by $h^*$, our assumption is contradictory. 

But I didn't quite get it.