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},
}