# Farkas' Lemma and Motzkin's Transposition Theorem

 Title: Farkas' Lemma and Motzkin's Transposition Theorem Authors: Ralph Bottesch, Max W. Haslbeck and René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at) Submission date: 2019-01-17 Abstract: We formalize a proof of Motzkin's transposition theorem and Farkas' lemma in Isabelle/HOL. Our proof is based on the formalization of the simplex algorithm which, given a set of linear constraints, either returns a satisfying assignment to the problem or detects unsatisfiability. By reusing facts about the simplex algorithm we show that a set of linear constraints is unsatisfiable if and only if there is a linear combination of the constraints which evaluates to a trivially unsatisfiable inequality. BibTeX: @article{Farkas-AFP, author = {Ralph Bottesch and Max W. Haslbeck and René Thiemann}, title = {Farkas' Lemma and Motzkin's Transposition Theorem}, journal = {Archive of Formal Proofs}, month = jan, year = 2019, note = {\url{https://isa-afp.org/entries/Farkas.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Jordan_Normal_Form, Simplex Used by: Linear_Programming 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.