ISARMATHLIB.ORG

IsarMathLib

A library of formalized mathematics for Isabelle/ZF theorem proving environment. This site is an experimental HTML rendering of fragments of the IsarMathLib. Project. IsarMathLib is a library of mathematical proofs formally verified by the Isabelle. Theorem proving environment. The formalization is based on the Zermelo-Fraenkel set theory. The Introduction. Provides more information about IsarMathLib. Mathematical notation on this site is rendered by MathJax. This page by Slawomir Kolodynski.

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IsarMathLib | isarmathlib.org Reviews

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A library of formalized mathematics for Isabelle/ZF theorem proving environment. This site is an experimental HTML rendering of fragments of the IsarMathLib. Project. IsarMathLib is a library of mathematical proofs formally verified by the Isabelle. Theorem proving environment. The formalization is based on the Zermelo-Fraenkel set theory. The Introduction. Provides more information about IsarMathLib. Mathematical notation on this site is rendered by MathJax. This page by Slawomir Kolodynski.

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5 finite1

6 finite zf 1

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8 partitions zf

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IsarMathLib | isarmathlib.org Reviews

https://isarmathlib.org

A library of formalized mathematics for Isabelle/ZF theorem proving environment. This site is an experimental HTML rendering of fragments of the IsarMathLib. Project. IsarMathLib is a library of mathematical proofs formally verified by the Isabelle. Theorem proving environment. The formalization is based on the Zermelo-Fraenkel set theory. The Introduction. Provides more information about IsarMathLib. Mathematical notation on this site is rendered by MathJax. This page by Slawomir Kolodynski.

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isarmathlib.org

1

IsarMathLib

http://www.isarmathlib.org/FinOrd_ZF.html

A library of formalized mathematics for Isabelle/ZF theorem proving environment. Finite ZF func ZF 1. This theory file contains properties of finite sets related to order relations. Part of this is similar to what is done in Finite ZF 1. Except that the development is based on the notion of finite powerset defined in Finite ZF. Rather the one defined in standard Isabelle Finite. Finite vs. bounded sets. The goal of this section is to show that finite sets are bounded and have maxima and minima. For linea...

2

IsarMathLib

http://www.isarmathlib.org/Introduction.html

A library of formalized mathematics for Isabelle/ZF theorem proving environment. This theory does not contain any formalized mathematics used in other theories, but is an introduction to IsarMathLib project. How to read IsarMathLib proofs - a tutorial. The first thing that mathematicians typically do is to define notions. In Isar this is done with the definition. Is used to denote both zero (of natural numbers) and the empty set, which is not surprising as those two things are the same in set theory.

3

IsarMathLib

http://www.isarmathlib.org/Nat_ZF_IML.html

A library of formalized mathematics for Isabelle/ZF theorem proving environment. Nat ZF IML imports. The induction lemmas in the standard Isabelle's Nat.thy file like for example nat induct. The next theorem is a version of induction on natural numbers that I was thought in school. A1: ( n in nat ) and. A2: ( P(0) ) and. A3: ( forall k in nat. P(k) longrightarrow P(succ(k) ). X in nat ), ( P(x) ). P(n) ) by (rule. A nonzero natural number has a predecessor. Nat ZF 1 L3:. A1: ( n in nat ) and. A2: ( foral...

4

IsarMathLib

http://www.isarmathlib.org/InductiveSeq_ZF.html

A library of formalized mathematics for Isabelle/ZF theorem proving environment. Nat ZF IML FiniteSeq ZF. In this theory we discuss sequences defined by conditions of the form (a 0 = x, a {n 1} = f(a n) ) and similar. Sequences defined by induction. First we define a helper notion of the sequence defined inductively up to a given natural number (n ). Text{InductiveSequenceN}(x,f,n) equiv ) ( text{The } a. a: succ(n) rightarrow domain(f) wedge a(0) = x wedge ( forall k in n. a(succ(k) = f(a(k) ) ). A a: s...

5

IsarMathLib

http://www.isarmathlib.org/Finite_ZF_1.html

A library of formalized mathematics for Isabelle/ZF theorem proving environment. Finite ZF 1 imports. Finite1 Order ZF 1a. This theory is based on Finite1. Theory and is obsolete. It contains properties of finite sets related to order relations. See the FinOrd. Theory for a better approach. Finite vs. bounded sets. The goal of this section is to show that finite sets are bounded and have maxima and minima. Finite set has a maximum - induction step. Finite ZF 1 1 L1:. A1: ( r text{ is total on } X ) and.

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slawekk.wordpress.com

FOM discussion | Formalized Mathematics

https://slawekk.wordpress.com/2014/10/25/fom-discussion

Just another WordPress.com weblog. Laquo; IsarMathLib 1.9.2 released. There is a very interesting discussion. About formalized mathematics going on the Foundations of Mathematics mailing list. The most interesting part of it (at least to me) is the thread about relative merits of Homotopy Type Theory. About this in the Bulletin of the American Mathematical Society. Here is a very simple statement which I often give to students as a first exercise in iteration, and to practice formal mathematics. This was...

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A library of formalized mathematics for Isabelle/ZF theorem proving environment. This site is an experimental HTML rendering of fragments of the IsarMathLib. Project. IsarMathLib is a library of mathematical proofs formally verified by the Isabelle. Theorem proving environment. The formalization is based on the Zermelo-Fraenkel set theory. The Introduction. Provides more information about IsarMathLib. Mathematical notation on this site is rendered by MathJax. This page by Slawomir Kolodynski.

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