A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Nine Chapters of Analytic Number Theory in Isabelle/HOL

2019
*
International Conference on Interactive Theorem Proving
*

Prime Number

doi:10.4230/lipics.itp.2019.16
dblp:conf/itp/Eberl19
fatcat:362y54hm75cmjjnykukb3u4a7i
*Theorem*The asymptotics*of*arithmetical functions such as the prime ω function, the divisor count σ0(n), and*Euler's*totient function ϕ(n) 2012 ACM Subject Classification Mathematics*of*computing ...*In*this paper, I present a formalisation*of*a large portion*of*Apostol's Introduction to Analytic Number Theory*in*Isabelle/HOL. ... Introduction The formalisation*of*Apostol's book*in*Isabelle/HOL started from the simple desire to have more properties about*Euler's*ϕ function available*in*the system. ...##
###
Mathematical Method and Proof

2006
*
Synthese
*

On a traditional view, the primary role

doi:10.1007/s11229-005-4064-5
fatcat:4ienrswtvzbetaw74oxyu7omzi
*of*a mathematical proof is to warrant the truth*of*the resulting*theorem*. ... I discuss a model*of*proof that is used*in*the automated deduction community, and show that this model does better*in*that respect. ... Proofs*of*Fermat's*theorem*, Lagrange's*theorem*, and Wilson's*theorem*can be found*in*almost any elementary textbook on number theory; see for example [31, 42] . 11*Euler's*proof assumed a slightly weaker ...##
###
A Formal Proof of the Minor-Exclusion Property for Treewidth-Two Graphs
[chapter]

2018
*
Lecture Notes in Computer Science
*

*Euler's*

*theorem*was

*formalized*

*in*

*Mizar*[15] . To the best

*of*our knowledge, the theory

*of*minors and tree decompositions was never

*formalized*. ... There are more

*formalizations*

*in*other interactive

*theorem*provers. For instance, planar graphs were

*formalized*

*in*Isabelle/HOL for the Flyspeck project [16] . ... Cite this paper as: Doczkal C., Combette G., Pous D.: A

*Formal*Proof

*of*the Minor-Exclusion Property for Treewidth-Two Graphs.

*In*: Avigad J., Mahboubi A. (eds) Interactive

*Theorem*Proving. ITP 2018. ...

##
###
Mizar in a Nutshell

unpublished

ACKNOWLEDGMENT The authors wish to express their sincere appreciation to the outstanding work

fatcat:htmhjetpubgwzbspup5a46tflm
*of*Andrzej Trybulec, the inventor*of**Mizar*and the leader*of*the*Mizar*project. ... As*of*now, also 53 facts from the Wiedijk's "Top 100 Mathematical*Theorems*" are*formalized*1 , such as Fundamental*Theorem**of*Algebra,*Euler's*Polyhedron Formula, Ramsey's*Theorem*, Sylow's*theorems*, and ... However, to state that a certain family*of*subsets is*in*fact a*partition*one needs to make a reference to the corresponding definitional*theorem*. ...##
###
Foundations of scientific research (Foundations of Research Activities)
[article]

2012
*
arXiv
*
pre-print

During years 2008 to 2011 author gives several courses on Foundations

arXiv:1212.1651v1
fatcat:e3oe5neztff5vjlj4trchbi3qa
*of*Scientific Research at Computer Science Faculty*of*the National Aviation University*in*Kiev. ... Some sections*of*the text contain enough material to lectures, but*in*some cases these are sketchs without references to Foundations*of*Research Activities. ... Some fundamental notions*of*the theory*of*Petri nets can be described*in**Mizar**formalism*. The*Mizar*Language is a*formal*language derived from the mathematical vernacular. ...##
###
Primality Testing is Polynomial-time: A Mechanised Verification of the AKS Algorithm
[article]

2019

The entire work is carried out

doi:10.25911/5f58b06ca124e
fatcat:objty3blpbbyha3evgeduua64a
*in*the HOL4*theorem*prover. The correctness*of*the AKS algorithm relies on a main*theorem*developed by the AKS team, based on the theory*of*finite fields. ... For the*formal*proof, we need to dive into several advanced topics*in*finite field,*in*particular the existence and uniqueness*of*finite fields, and properties*of*cyclotomic polynomials. ... (*Euler's*Totient*Theorem*). ...