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Canonical Big Operators

Abstract : In this paper, we present an approach to describe uniformly iterated “big” operations and to provide lemmas that encapsulate all the commonly used reasoning steps on these constructs. We show that these iterated operations can be handled generically using the syntactic notation and canonical structure facilities provided by the Coq system. We then show how these canonical big operations played a crucial enabling role in the study of various parts of linear algebra and multi-dimensional real analysis, as illustrated by the formal proofs of the properties of determinants, of the Cayley-Hamilton theorem and of Kantorovitch's theorem.
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https://hal.inria.fr/inria-00331193
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Submitted on : Wednesday, October 15, 2008 - 4:04:12 PM
Last modification on : Saturday, June 25, 2022 - 10:59:58 PM
Long-term archiving on: : Tuesday, October 9, 2012 - 1:50:08 PM

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Yves Bertot, Georges Gonthier, Sidi Ould Biha, Ioana Pasca. Canonical Big Operators. Theorem Proving in Higher Order Logics, Aug 2008, Montreal, Canada. ⟨10.1007/978-3-540-71067-7⟩. ⟨inria-00331193⟩

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