A logical approach to discrete math
A logical approach to discrete math
Inductive Definitions: Automation and Application
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
A Compendium of Continuous Lattices in MIZAR
Journal of Automated Reasoning
On the Integrity of a Repository of Formalized Mathematics
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
Computer proofs about finite and regular sets: the unifying concept of subvariance
Journal of Symbolic Computation - Special issue: First order theorem proving
Presenting and Explaining Mizar
Electronic Notes in Theoretical Computer Science (ENTCS)
Narrative Structure of Mathematical Texts
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Adapting functional programs to higher order logic
Higher-Order and Symbolic Computation
An integrated proof language for imperative programs
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
ATP cross-verification of the Mizar MPTP challenge problems
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Improving the usability of HOL through controlled automation tactics
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Information retrieval and rendering with MML query
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
XML-izing mizar: making semantic processing and presentation of MML easy
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Transformations of MML database’s elements
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Journal of Automated Reasoning
The Mizar Mathematical Library in OMDoc: Translation and Applications
Journal of Automated Reasoning
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Four statements equivalent to well-foundedness (well-founded induction, existence of recursively defined functions, uniqueness of recursively defined functions, and absence of descending ω-chains) have been proved in Mizar and the proofs mechanically checked for correctness. It seems not to be widely known that the existence (without the uniqueness assumption) of recursively defined functions implies well-foundedness. In the proof we used regular cardinals, a fairly advanced notion of set theory. The theory of cardinals in Mizar was developed earlier by G. Bancerek. With the current state of the Mizar system, the proofs turned out to be an exercise with only minor additions at the fundamental level. We would like to stress the importance of a systematic development of a mechanized data base for mathematics in the spirit of the QED Project. 12pt ENOD – Experience, Not Only Doctrine G. Kreisel