The core of the argument lies in the selection of a subset of transactions that maximizes the fee rate while adhering to certain inclusion and exclusion criteria, specifically focusing on a set labeled $pot$. A lemma introduced posits that $pot$ is unique in being the highest fee rate set among all possible sets that include a specific transaction ($inc$) and exclude another ($exc$). Furthermore, it states that a transaction $t$ belongs to $pot$ if and only if its fee rate is higher than the overall fee rate of $pot$.

The proposition extends this discussion by considering an element $B$, which maximizes the fee rate within a defined collection of topologically valid sets that include $inc$ and are exclusive of $exc$. It asserts that if a subset $C$ of $pot$ is topologically valid, then it must be included within $B$. A proof by contradiction is presented to support this proposition, arguing that if there exists a subset $C$ within $pot$ that is topologically valid but not included in $B$, it would imply the existence of a transaction with a fee rate higher than that of $B$, contradicting the initial definition of $B$ as maximizing the fee rate. The argument concludes that since adding such a transaction to $B$ would result in a higher fee rate while maintaining topological validity, the original assumption must be incorrect, thereby supporting the initial proposition.

This analysis underlines the intricate relationship between transaction selection based on fee rates and the structural constraints imposed by transaction dependencies, offering insights into how transaction subsets can be optimized within a blockchain framework.