# Graph Lemma

 Title: Graph Lemma Authors: Štěpán Holub and Štěpán Starosta Submission date: 2021-05-24 Abstract: Graph lemma quantifies the defect effect of a system of word equations. That is, it provides an upper bound on the rank of the system. We formalize the proof based on the decomposition of a solution into its free basis. A direct application is an alternative proof of the fact that two noncommuting words form a code. BibTeX: @article{Combinatorics_Words_Graph_Lemma-AFP, author = {Štěpán Holub and Štěpán Starosta}, title = {Graph Lemma}, journal = {Archive of Formal Proofs}, month = may, year = 2021, note = {\url{https://isa-afp.org/entries/Combinatorics_Words_Graph_Lemma.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Combinatorics_Words Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.