This proposition suggests a foundational principle in computational theory, particularly relevant in the context of algorithms that manipulate sequences or structures in a linear fashion. The concept of 'prefix-intersection merging' refers to an operation that combines two sequences by intersecting their prefixes in such a way that the resulting sequence maintains or exceeds the order and elements of the original sequences.

Understanding this process involves exploring the mathematical and logical underpinnings that govern how sequences are merged, ensuring that the integrity and hierarchical ordering of elements are preserved or enhanced. This principle may have far-reaching implications in fields like data structure optimization, algorithm design, and computational efficiency, where maintaining or improving the sequential order of elements is crucial.

Exploring the validity of this assertion could lead to significant advancements in our understanding of sequence manipulation and intersection algorithms. By proving this principle, one could establish a foundational rule that aids in the development of more efficient computational methods, potentially impacting various applications from database management systems to information retrieval processes.

In essence, the discussion points towards a deeper investigation into the mechanics of prefix-interception merging, urging for a proof or theoretical validation that supports the initial claim. Such a proof would not only clarify the operations of these algorithms but also contribute to the broader field of computer science by providing insights into the optimization of sequential data processing and analysis.