Which mathematical definitions should be formalised in Lean?

The question. Which mathematical objects would you like to see formally defined in the Lean Theorem Prover?

Tutorials for formalizing mathematical definitions/statements in Lean

One can of course also look into mathlib for examples, but most of the time this just shows me what a good formalization looks like but not ...

The three kinds of types — Formalising Mathematics 0.1 ...

In Lean the corresponding type is called X → Y so you can think of the → symbol as “the way to make this type”. We make terms of this type using something ...

2. Basics — Mathematics in Lean 0.1 documentation

Notice that the proof does not begin with by : an expression that begins with calc is a proof term. A calc expression can also be used inside a tactic proof, ...

Mathematics in Lean

... will write mathematical definitions, theorems, and ... Universal quantifiers are often hidden in definitions, and Lean will unfold definitions to expose them when ...

Classes — Formalising Mathematics 0.1 documentation

... definition of a group in Lean's maths library). ... With classes, the idea is that a “magic” system which we don't have to think about (Lean's typeclass system) ...

ProofLab: A Short Introduction to Formalising Mathematics in Lean

As always, a theory consists of definitions, theorems, and examples. Being precise and well-structured in this phase, will simplify the formalisation step.

Lean is better for proper maths than all the other theorem provers

Think of any piece of what my “proper maths” colleagues would call respectable mathematics — e.g. formalising the definition of an algebraic ...

Mathematics in Lean - Floris van Doorn

An proof assistant or interactive theorem prover is a program that can reason with mathematical definitions, theorems and proofs, provided a ...

Why typeclasses rather than inductive types to define mathematical ...

It seems sensible to me to formalize mathematical structures this way, since the Lean keyword “structure” essentially creates a cartesian ...

Kevin Buzzard got a research grant to begin the proof of formalising ...

"Such a project will enable Lean to understand many of the basic definitions in modern number theory and arithmetic geometry, meaning that it ...

Formalising mathematics : workshop 3 — sequences and limits | Xena

Every definition in Lean comes with a cost. Last week we saw some of this cost. We didn't use Lean's inbuilt group definition, we rolled our own ...

1. Introduction — Mathematics in Lean 0.1 documentation

Put simply, Lean is a tool for building complex expressions in a formal language known as dependent type theory. Every expression has a type, and you can use ...

Lean (proof assistant) - Wikipedia

As of September 2024, mathlib had formalised over 165,000 theorems and 85,000 definitions in Lean. ... formalizing a result at the cutting edge of mathematical ...

Formal Methods in Mathematics and the Lean Theorem Prover

terms. • Claims rely on background mathematical knowledge. I will focus on mathematics: • Problems are conceptually ...

Exploring Formalisation - Clara Löh - Universität Regensburg

Proof assistants allow us to formalise mathematical definitions, examples, ... mathematical basics is formalised, this will change. There ...

Introduction - Theorem Proving in Lean 4

Lean can not only define mathematical objects and express mathematical assertions in dependent type theory, but it also can be used as a language for ...

Full article: Schemes in Lean - Taylor & Francis Online

Scheme · lean · formal proof · Previous article ...

Terence Tao is formalizing his recent paper in Lean. While working ...

For example we could define the natural numbers inductively ... You can "formalize" nontrivial mathematical statements, say, from analysis.

Formalizing chemical physics using the Lean theorem prover

When a mathematical object is formally defined in Lean, multiple theorems can be written about it with certainty that all proofs pertain to the ...