### 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.

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