Abstract
In this paper, we present an approach to describe uniformly iterated “big” operations, like \(\sum_{i=0}^n f(i)\) or max i ∈ I f(i) 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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Bertot, Y., Gonthier, G., Ould Biha, S., Pasca, I. (2008). Canonical Big Operators. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2008. Lecture Notes in Computer Science, vol 5170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71067-7_11
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DOI: https://doi.org/10.1007/978-3-540-71067-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71065-3
Online ISBN: 978-3-540-71067-7
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