### Linear Inequalities

Ralph Bottesch, Alban Reynaud, René ThiemannArchive of Formal Proofs 2019.

### 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{http://isa-afp.org/entries/Linear_Inequalities.html}, Formal proof development}, ISSN = {2150-914x}, }