# Linear Inequalities

 Title: Linear Inequalities Authors: Ralph Bottesch, Alban Reynaud and René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at) Submission date: 2019-06-21 Abstract: We formalize results about linear inqualities, mainly from Schrijver's book. The main results are the proof of the fundamental theorem on linear inequalities, Farkas' lemma, Carathéodory's theorem, the Farkas-Minkowsky-Weyl theorem, the decomposition theorem of polyhedra, and Meyer's result that the integer hull of a polyhedron is a polyhedron itself. Several theorems include bounds on the appearing numbers, and in particular we provide an a-priori bound on mixed-integer solutions of linear inequalities. BibTeX: @article{Linear_Inequalities-AFP, author = {Ralph Bottesch and Alban Reynaud and René Thiemann}, title = {Linear Inequalities}, journal = {Archive of Formal Proofs}, month = jun, year = 2019, note = {\url{https://isa-afp.org/entries/Linear_Inequalities.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: LLL_Basis_Reduction 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.