Farkas' Lemma and Motzkin's Transposition Theorem

Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐

January 17, 2019


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.
BSD License


Theories of Farkas