# About facets and aggregated inequalities

 4 Consider the following claim: Suppose you have two distinct valid inequalities $$ax \le b$$ and $$cx \le d$$. Further suppose that your polyhedron is full-dimensional. Then the aggregated inequality $$(a+c)x \le (b+d)$$ cannot induce a facet. This claim is true, and I have used it in my research. However, I was hoping to find it explicitly stated in literature. Other researchers have referred me to Schrijver's Theory of LP and IP, but I cannot seem to find it. (Perhaps it is too trivial a result to include.) Is this claim made in any published material? asked 29 Jul '14, 16:30 Austin Buchanan 1.3k●3●13 accept rate: 42%

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 2 It seems to me that this is an easy consequence of the fact that the set of facets forms a minimal description of the polyhedron, so removing one must produce a strictly larger polyhedron. That can't be true of an aggregated inequality if the component inequalities are part of the description. answered 30 Jul '14, 19:25 Matthew Salt... ♦ 4.7k●3●10 accept rate: 17%
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Asked: 29 Jul '14, 16:30

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Last updated: 30 Jul '14, 19:25

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