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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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]
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)