Formalizing Convex Hull Algorithms
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Higher-Order Intuitionistic Formalization and Proofs in Hilbert's Elementary Geometry
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Robustness in CAD Geometric Constructions
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
Journal of Symbolic Computation
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic
Journal of Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Formalizing Desargues' theorem in Coq using ranks
Proceedings of the 2009 ACM symposium on Applied Computing
Mathematical quotients and quotient types in Coq
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
The not so simple proof-irrelevant model of CC
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Mechanical theorem proving in Tarski's geometry
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Mechanical theorem proving in computational geometry
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
Formalizing Desargues' theorem in Coq using ranks
Proceedings of the 2009 ACM symposium on Applied Computing
Management of geometric knowledge in textbooks
Data & Knowledge Engineering
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
A coherent logic based geometry theorem prover capable of producing formal and readable proofs
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Journal of Automated Reasoning
A case study in formalizing projective geometry in Coq: Desargues theorem
Computational Geometry: Theory and Applications
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We investigate how projective plane geometry can be formalized in a proof assistant such as Coq. Such a formalization increases the reliability of textbook proofs whose details and particular cases are often overlooked and left to the reader as exercises. Projective plane geometry is described through two different axiom systems which are formally proved equivalent. Usual properties such as decidability of equality of points (and lines) are then proved in a constructive way. The duality principle as well as formal models of projective plane geometry are then studied and implemented in Coq. Finally, we formally prove in Coq that Desargues' property is independent of the axioms of projective plane geometry.