T. De and . Zenon, Le problème est formellement exprimé comme suit : ?x, y, z (distinct_points(x, y) ? incident_point_and_line(x, z) ? incident_point_and_line(y, z) ? equal_lines(z, line_connecting

L. Étapes-commençant-par and «. Axiom, sont des feuilles de l'arbre de preuve. En suivant cette preuve, il est possible de construire la preuve suivante : ? Étant donnés les points T4, T6 (étape 3), et la droite T8 (étape 4) tels que H10: distinct_points(T4,T6)

T. Avec, T. , and T. , T6) (étapes 8 à 11), nous devons montrer le but précédent (H14 niée) dans les cas suivants : 1, nous avons aussi H10: distinct_points(T4,T6), ce qui est absurde

H. Étant-donné, T6)), c'est exactement le 6.5. TRACES DE SUPER ZENON fof(geometry_conjecture, conjecture, => equal_lines (Z, line_connecting(X, Y)))))

]. Abrial, The B-Book, Assigning Programs to Meanings, pp.24-47, 1996.

J. Abrial, Modeling in Event-B -System and Software Engineering, 2010.

J. Abrial and D. Cansell, Click???n Prove: Interactive Proofs within Set Theory, Lecture Notes in Computer Science, vol.2758, pp.1-24, 2003.
DOI : 10.1007/10930755_1

URL : https://hal.archives-ouvertes.fr/inria-00099836

J. Abrial and L. Mussat, On Using Conditional Definitions in Formal Theories, pp.242-269
DOI : 10.1007/3-540-45648-1_13

M. Armand, G. Faure, B. Grégoire, C. Keller, L. Théry et al., A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses, Lecture Notes in Computer Science, vol.53, issue.6, pp.135-150, 2011.
DOI : 10.1145/1217856.1217859

URL : https://hal.archives-ouvertes.fr/hal-00639130

M. Armand, G. Faure, B. Grégoire, C. Keller, L. Thery et al., A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses, Certified Programs and Proofs 2011 of Lecture notes in computer science -LNCS, pp.135-150, 2011.
DOI : 10.1145/1217856.1217859

URL : https://hal.archives-ouvertes.fr/hal-00639130

H. Barendregt and A. M. Cohen, Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants, Journal of Symbolic Computation, vol.32, issue.1-2, pp.3-22, 2001.
DOI : 10.1006/jsco.2001.0455

C. Barrett and C. Tinelli, CVC3, Proceedings of the 19 th International Conference on Computer Aided Verification (CAV '07), pp.298-302, 2007.
DOI : 10.1007/978-3-540-73368-3_34

K. Berkani, C. Dubois, A. Faivre, and J. Falampin, Validation des r??gles de base de l'Atelier B, Techniques et sciences informatiques, vol.23, issue.7, pp.855-878, 2004.
DOI : 10.3166/tsi.23.855-878

D. Bert, J. P. Bowen, M. C. Henson, and K. Robinson, Formal Specification and Development in Z and, 2nd International Conference of B and Z Users Proceedings, volume 2272 of Lecture Notes in Computer Science, p.176, 2002.

F. Besson, P. Fontaine, and L. Théry, A Flexible Proof Format for SMT : a Proposal
URL : https://hal.archives-ouvertes.fr/hal-00642544

E. W. Beth, Semantic Entailment and Formal Derivability, Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen, vol.18, issue.13 101, pp.309-342, 1955.

F. Bobot, S. Conchon, E. Contejean, and S. Lescuyer, Implementing polymorphism in SMT solvers, Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning, SMT '08/BPR '08, p.32, 2008.
DOI : 10.1145/1512464.1512466

J. Bodeveix and M. Filali, Type Synthesis in B and the Translation of B to PVS, pp.350-369
DOI : 10.1007/3-540-45648-1_18

S. Böhme and T. Nipkow, Sledgehammer: Judgement Day, Lecture Notes in Computer Science, vol.6173, pp.107-121
DOI : 10.1007/978-3-642-14203-1_9

R. Bonichon, TaMeD: A Tableau Method for Deduction Modulo, Lecture Notes in Computer Science, vol.3097, pp.445-459, 2004.
DOI : 10.1007/978-3-540-25984-8_33

R. Bonichon, D. Delahaye, and D. Doligez, Zenon: An Extensible Automated Theorem Prover Producing Checkable Proofs, Dershowitz and Voronkov [35], pp.151-165
DOI : 10.1007/978-3-540-75560-9_13

URL : https://hal.archives-ouvertes.fr/inria-00315920

]. R. Bonichon and O. Hermant, A Semantic Completeness Proof for TaMeD, LNCS, vol.19, issue.4246, pp.141-167, 2006.
DOI : 10.1007/11916277_12

URL : https://hal.archives-ouvertes.fr/hal-01337086

R. J. Boulton, A. D. Gordon, M. J. Gordon, J. Harrison, J. Herbert et al., Experience with Embedding Hardware Description Languages in HOL, TPCD, volume A-10 of IFIP Transactions, pp.129-156, 1992.

P. Brauner, C. Houtmann, and C. Kirchner, Principles of Superdeduction, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), pp.41-50, 2007.
DOI : 10.1109/LICS.2007.37

URL : https://hal.archives-ouvertes.fr/inria-00133557

L. Burdy, Traitement des expressions dépourvues de sens de la théorie des ensembles : Application à la méthode B, p.96, 2000.

G. Burel, Unbounded Proof-Length Speed-Up in Deduction Modulo, Computer Science Logic, pp.496-511, 2007.
DOI : 10.1007/978-3-540-74915-8_37

URL : https://hal.archives-ouvertes.fr/inria-00138195

P. Chartier, Formalisation of B in Isabelle/HOL, LNCS, vol.1393, pp.66-82, 1998.
DOI : 10.1007/BFb0053356

A. Ciabattoni, N. Galatos, and K. Terui, From Axioms to Analytic Rules in Nonclassical Logics, 2008 23rd Annual IEEE Symposium on Logic in Computer Science, pp.229-240, 2008.
DOI : 10.1109/LICS.2008.39

H. Cirstea and C. Kirchner, Using Rewriting and Strategies for Describing the B Predicate Prover, Strategies in Automated Deduction, pp.25-36, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00098748

. Clearsy, Guide de rédaction de règles mathématiques, p.40

. Clearsy, Atelier B 4.0, Feb, p.37, 2009.

J. Coleman, C. Jones, I. Oliver, A. Romanovsky, and E. Troubitsyna, RODIN (Rigorous Open Development Environment for Complex Systems), EDCC-5, pp.23-26, 2005.

S. Colin and G. Mariano, Coq, l'alpha et l'omega de la preuve pour B ?, p.31, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00361302

L. M. De-moura and N. Bjorner, Z3: An Efficient SMT Solver, TACAS, pp.337-340, 2008.
DOI : 10.1007/978-3-540-78800-3_24

D. Déharbe, P. Fontaine, Y. Guyot, and L. Voisin, SMT Solvers for Rodin, pp.194-207
DOI : 10.1007/978-3-642-30885-7_14

D. Delahaye, A Tactic Language for the System Coq, Logic for Programming and Automated Reasoning (LPAR), pp.85-95, 2000.
DOI : 10.1007/3-540-44404-1_7

URL : https://hal.archives-ouvertes.fr/hal-01125070

D. Delahaye and M. Jacquel, Recovering Intuition from Automated Formal Proofs using Tableaux with Superdeduction, Electronic Journal of Mathematics & Technology, pp.2013-2034
URL : https://hal.archives-ouvertes.fr/hal-01099371

G. Dowek, T. Hardin, and C. Kirchner, Theorem Proving Modulo, Journal of Automated Reasoning, vol.31, issue.1, pp.33-72, 2003.
DOI : 10.1023/A:1027357912519

URL : https://hal.archives-ouvertes.fr/hal-01199506

P. Fontaine, J. Marion, S. Merz, L. P. Nieto, and A. F. Tiu, Expressiveness + Automation + Soundness: Towards Combining SMT Solvers and Interactive Proof Assistants, Lecture Notes in Computer Science, vol.29, issue.3-4, pp.167-181, 2006.
DOI : 10.1007/3-540-45620-1_26

URL : https://hal.archives-ouvertes.fr/inria-00001088

M. J. Gordon, R. Milner, C. P. Wadsworth39-]-k, and . Hintikka, Form and Content in Quantification Theory, IFIP TCS, pp.33-40, 1955.

C. Houtmann, Représentation et interaction des preuves en superdéduction modulo, 0118.

M. Jacquel, K. Berkani, D. Delahaye, and C. Dubois, Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving, SEFM, pp.253-268, 2011.
DOI : 10.1007/3-540-45648-1_8

URL : https://hal.archives-ouvertes.fr/hal-00722373

M. Jacquel, K. Berkani, D. Delahaye, and C. Dubois, Tableaux Modulo Theories Using Superdeduction, Lecture Notes in Computer Science, vol.7364, issue.21, pp.332-338, 2012.
DOI : 10.1007/978-3-642-31365-3_26

URL : https://hal.archives-ouvertes.fr/hal-01099338

M. Jacquel, K. Berkani, D. Delahaye, and C. Dubois, Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving, Software and Systems Modeling (SoSyM), 2013. À paraître, p.101
DOI : 10.1007/3-540-45648-1_8

URL : https://hal.archives-ouvertes.fr/hal-00722373

É. Jaeger and C. Dubois, Why Would You Trust B ? In Dershowitz and Voronkov, pp.288-302

K. Korovin, iProver ??? An Instantiation-Based Theorem Prover for First-Order Logic (System Description), IJ- CAR, pp.292-298, 2008.
DOI : 10.1007/978-3-540-71070-7_24

É. and L. Lay, Automatiser la validation des règles, INSA (Rennes), vol.59, p.64, 2008.

M. Leuschel and M. J. Butler, ProB: an automated analysis toolset for the B method, International Journal on Software Tools for Technology Transfer, vol.49, issue.3, pp.185-203, 2008.
DOI : 10.1007/s10009-007-0063-9

I. Maamria, M. Butler, A. Edmunds, and A. Rezazadeh, On an Extensible Rule-Based Prover for Event-B, Lecture Notes in Computer Science, vol.5977, issue.38, pp.407-454, 2010.
DOI : 10.1007/978-3-642-11811-1_40

D. Mentré, C. Marché, J. Filliâtre, and M. Asuka, Discharging Proof Obligations from Atelier??B Using Multiple Automated Provers, Derrick et al. [34], pp.238-251
DOI : 10.1007/978-3-642-30885-7_17

S. Merz and H. Vanzetto, Automatic Verification of TLA???+??? Proof Obligations with SMT Solvers, Lecture Notes in Computer Science, vol.7180, issue.32, pp.289-303, 2012.
DOI : 10.1007/978-3-642-28717-6_23

URL : https://hal.archives-ouvertes.fr/hal-00760570

S. Negri and J. Plato, Abstract, Bulletin of Symbolic Logic, vol.4, issue.04, pp.418-435, 1998.
DOI : 10.2307/420956

D. Pastre, Strong and weak points of the MUSCADET theorem prover -examples from CASC-JC, Journal of AI Communications, vol.15, issue.2-3, pp.147-160, 2002.

D. Prawitz, Natural Deduction. A Proof-Theoretical Study, Stockholm Studies in Philosophy, vol.3, p.116, 1965.

A. Riazanov and A. Voronkov, The design and implementation of Vampire, Journal of AI Communications, vol.15, issue.32, pp.91-110, 2002.

R. M. Smullyan, First-Order Logic, p.101, 1968.
DOI : 10.1201/b10689-23

. Steria, Guide méthodologique de validation de la base de règles de l, Atelier B, p.46, 1996.

G. Sutcliffe, The TPTP Problem Library and Associated Infrastructure, Journal of Automated Reasoning, vol.13, issue.2, pp.337-362, 2009.
DOI : 10.1007/s10817-009-9143-8

C. Weidenbach, D. Dimova, A. Fietzke, R. Kumar, M. Suda et al., SPASS Version 3.5, Lecture Notes in Computer Science, vol.18, issue.2-4, pp.140-145, 2009.
DOI : 10.1007/978-3-540-73595-3_38

W. Windsteiger, An automated prover for Zermelo???Fraenkel set theory in Theorema, Journal of Symbolic Computation, vol.41, issue.3-4
DOI : 10.1016/j.jsc.2005.04.013