Abstract
We describe two formal proofs of the finite version of Hall’s Marriage Theorem performed with the proof assistant Isabelle/HOL, one by Halmos and Vaughan and one by Rado. The distinctive feature of our formalisation is that instead of sequences (often found in statements of this theorem) we employ indexed families, thus avoiding tedious reindexing of sequences.
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References
Aigner, M., Ziegler, G.M.: Proofs from the Book. Springer, Heidelberg (2001)
Easterfield, T.E.: A combinatorial algorithm. Journal London Mathematical Society 21, 219–226 (1946)
Everett, C.J., Whaples, G.: Represetations of sequences of sets. American Journal of Mathematics 71, 287–293 (1949)
Hall, P.: On representatives of subsets. Journal London Mathematical Society 10, 26–30 (1935)
Halmos, P.R., Vaughan, H.E.: The marriage problem. American Journal of Mathematics 72, 214–215 (1950)
Jiang, D., Nipkow, T.: Hall’s marriage theorem. In: Klein, G., Nipkow, T., Paulson, L. (eds.) The Archive of Formal Proofs (December 2010), http://afp.sf.net/entries/Marriage.shtml ; formal proof development
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Rado, R.: Note on the transfinite case of Hall’s Theorem on representatives. Journal London Mathematical Society 42, 321–324 (1967)
Romanowicz, E., Grabowski, A.: The Hall marriage theorem. Formalized Mathematics 12(3), 315–320 (2004)
Wikipedia: Hall’s marriage theorem — wikipedia, the free encyclopedia (2011), en.wikipedia.org/w/index.php?title=Hall%27s_marriage_theorem&oldid=419179777 (accessed September 8, 2011]
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Jiang, D., Nipkow, T. (2011). Proof Pearl: The Marriage Theorem. In: Jouannaud, JP., Shao, Z. (eds) Certified Programs and Proofs. CPP 2011. Lecture Notes in Computer Science, vol 7086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25379-9_28
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DOI: https://doi.org/10.1007/978-3-642-25379-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25378-2
Online ISBN: 978-3-642-25379-9
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