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A proof theory for generic judgments
ACM Transactions on Computational Logic, 2005The operational semantics of a computation system is often presented as inference rules or, equivalently, as logical theories. Specifications can be made more declarative and high level if syntactic details concerning bound variables and substitutions are encoded directly into the logic using term-level abstractions (λ-abstraction) and ...
Dale Miller 0001, Alwen Tiu
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A Pattern in Number Theory: Example→ Generalization→ Proof
The Mathematics Teacher, 1971The study of patterns is an integral part of the study of mathematics. As we teach mathematics, we must point out how to search for patterns and how patterns may aid us in problem solving. The following problem is one that combines patterns, ideas from number theory, and mathematical induction: “Prove that it is possible to pay, without requiring ...
David R. Duncan, Bonnie H. Litwiller
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Generalization in Type Theory Based Proof Assistants
2002This paper describes a mechanism to generalize mathematical results in type theory based proof assistants. The proposed mechanism starts from a proved theorem or a proved set of theorems (a theory) and makes it possible to get less specific results that can be instantiated and reused in other contexts.
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A generalization of the proof of the triviality of scalar field theories
Journal of Mathematical Physics, 1983The proof of the triviality of φ4 theory in d>4 dimensions is generalized. We show that the triviality of scalar field theories holds for a wide class of potentials.
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Secondary teachers’ knowledge of elementary number theory proofs: the case of general-cover proofs
Journal of Mathematics Teacher Education, 2011In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements?
Michal Tabach +5 more
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Computer-generated conjectures(!) and proofs(!!) in combinatorial game theory (abstract only)
ACM Communications in Computer Algebra, 2008The rapidly growing activity of experimental mathematics is still, to a large extent, a straightforward (albeit far-reaching) extension of the usual mode of paper-and-pencil research, where the pencil just got so much quicker and sharper and the paper so much larger.
Doron Zeilberger +1 more
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Proofs for the general theory of classical electrodynamics
2017Mathematical proofs are given for the majority of equations relating to the gen- eral theory of classical electrodynamics. These include equations for the static magnetic vector and scalar fields, the Lorenz condition, power- and force densities, magnetostatic power- and force densities and far field expressions like Jefimenko’s expressions.
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Generic power of number theory proofs
2022To design generic proving multiple proof tasks, we use an epistemological tool in which the idea of generic power plays a crucial role. Thanks to a number theory case, we show how it works and then we open the discussion in a didactical way focusing on the Secondary-Tertiary transition.
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Towards A Foundation of A General Proof Theory
1973Publisher Summary This chapter discusses general proof theory. The name proof theory was originally given by Hilbert to a constructive study of proofs with certain specific aims. By such a study, the consistency of mathematics is established or, more generally, a reduction of mathematics to a certain constructive part is obtained. Hence, the study of
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