This theorem posits an interesting approach to understanding how data can be efficiently compressed and later restored without loss of information or fidelity. The equations presented provide a mathematical framework that supports this theory, suggesting that the compression of a combined dataset (A + B) is equal to the compression of one part added to the compression of the other (C(A) + C(B)). Moreover, it implies that this combined compression is always greater than or equal to the sum of its parts.

These formulas encapsulate key principles in the field of data compression, highlighting the inherent efficiency and potential gains in compressing data together rather than separately. This concept not only underscores the mathematical underpinnings of data compression algorithms but also emphasizes the importance of considering the interplay between different datasets when seeking to optimize compression strategies. By examining the relationship between the compression of combined and individual datasets, the theorem provides a basis for further exploration into more effective and efficient data compression techniques, which could have profound implications for data storage, transmission, and processing technologies.