Computational support for case-heavy proofs in mathematical phylogenetics

TL;DR

This paper shows how computational methods can simplify complex case-heavy proofs in mathematical phylogenetics and introduces new lemmas that are difficult to prove manually.

Contribution

It demonstrates the use of computational support to streamline proofs and presents new combinatorial lemmas in the field.

Findings

Computational techniques reduce proof complexity in phylogenetics.

New combinatorial lemmas are proven using these methods.

Potential for wider application in phylogenetics research.

Abstract

In this note we demonstrate that a number of case-heavy combinatorial proofs in the mathematical phylogenetics literature can be proven more compactly using computational support. We use these techniques to also prove several new combinatorial lemmas that would have taken considerable effort to prove by hand. We are optimistic that similar approaches can be deployed more widely in phylogenetics.