D. Amir and . Aczel, Fermat's last theorem: unlocking the secret of an ancient mathematical problem. Four Walls Eight Windows, 1996.

Y. Bertot and P. Casteran, Interactive Theorem Proving and Program Development, 2004.
DOI : 10.1007/978-3-662-07964-5

URL : https://hal.archives-ouvertes.fr/hal-00344237

M. Daumas, G. Melquiond, and C. Muñoz, Guaranteed Proofs Using Interval Arithmetic, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), 2005.
DOI : 10.1109/ARITH.2005.25

URL : https://hal.archives-ouvertes.fr/hal-00164621

D. Gage and J. Mccormick, We did nothing wrong, Baseline, vol.1, issue.28, pp.32-58, 2004.

L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied interval analysis, 2001.
DOI : 10.1007/978-1-4471-0249-6

URL : https://hal.archives-ouvertes.fr/hal-00845131

J. Lions, Ariane 5 flight 501 failure report by the inquiry board, 1996.

K. Makino and M. Berz, Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, vol.4, issue.4, pp.379-456, 2003.

R. E. Moore, Interval analysis, 1966.

A. Neumaier, Interval methods for systems of equations, 1990.
DOI : 10.1017/CBO9780511526473

S. Owre, J. M. Rushby, and N. Shankar, PVS: A prototype verification system, 11th International Conference on Automated Deduction, pp.748-752, 1992.
DOI : 10.1007/3-540-55602-8_217

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.2627

E. Philip and . Ross, The exterminators, IEEE Spectrum, vol.42, issue.9, pp.36-41, 2005.

J. Rushby and F. Henke, Formal verification of algorithms for critical systems, Proceedings of the Conference on Software for Critical Systems, pp.1-15, 1991.

A. Tiwari, N. Shankar, and J. Rushby, Invisible formal methods for embedded control systems, Proceedings of the IEEE, vol.91, issue.1, pp.29-39, 2003.
DOI : 10.1109/JPROC.2002.805818

I. Unité-de-recherche and I. Rhône, Alpes 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex (France) Unité de recherche, 2004.

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399