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All the Lean code (the juicy stuff) is contained in the directory src/. ![]() You can open it by clicking on one of the icons in the top right hand corner. You can step through the proof line-by-line,Īnd see the internals of Lean's "brain" in the Goal window. "Goal view": in the event that you would like to read a proof,.This also works by Ctrl-clicking on the name. (such as Lbar, or Tinv_continuous), then you can choose "Go to definition" from the menu,Īnd you will be taken to the relevant location in the source files. "Go to definition": If you right-click on a name of a definition or lemma.There are two pieces of functionality that help a lot when browsing through Lean code: You are all set to start exploring the code. Will save you some time by not havig to do leanproject build. #Liquid notes ilok downloadIn the folder lean-liquid will download the olean files created by our continuous integration. #Liquid notes ilok how toTo install Lean and a supporting toolchain.Īfter that, download and open a copy of the repositoryīy executing the following command in a terminal:įor detailed instructions on how to work with Lean projects, To install a Lean development environment on your computer please use the To use it, simply click the Gitpod button at the top of this Readme file. Gitpod provides an online Lean environment, but requires a GitHub accountĪnd might have weaker performance than a local installation. Getting the projectĪt the moment, we support two ways of browsing this repository:Įither via Gitpod or by using a Lean development environment.Ĭrucially, both methods will allow you to introspect Lean's "Goal state" during proofs,Īnd easily jump to definitions or otherwise follow paths through the code. Of the main ingredients in the repository.Īll material in the blueprint is cross-referenced with the Lean formalization using hyperlinks. Variables (p' p : ℝ≥ 0) [fact ( 0 0, Ext i (ℳ_ S) V ≅ 0 := How to browse this repository Blueprintīelow we explain how to engage with the Lean code directly. The statement can be found in src/liquid.lean #Liquid notes ilok verificationTogether, the two components give a formal verification of Theorem 1.1 of the blogpost. The second half of the project was completed on 14th July 2022. The preliminary announcement of a proof of Theorem 9.4 was made on 28th May 2021, by Johan Commelin and his team from the Lean prover community. The blueprint was a guide which was comprehensible to mathematicians who had no Lean training, whilst also being a visual guide to where progress was needed during the formalisation process. "Prove Analytic 9.4" and "Prove that Analytic 9.4 implies Theorem 1.1"Īn important intermediate achievement was the completion of a blueprint for the proof of 9.4 and the related 9.5. The project then split into two sub-projects: When the project started, it was immediately noticed that there was a "sub-boss" in the form of Analytic 9.4, a far more technical theorem involving a completely different class of objects and which Scholze was claiming was a sufficiently powerful stepping stone. ![]() The challenge in the blog post is to formalise its Theorem 1.1, a variant of Analytic 9.1 (i.e. Although Lean 4's type theory is the same as Lean 3's type theory, it currently lacks the mathematical infrastructure needed for this project. Our formalisation could not have even started without a major classical mathematical library backing it up, and so we chose Lean 3 as the engine behind the project. Lean is a project being developed at Microsoft Research by Leonardo de Moura and his team. The formal system which we are using as a target system is Lean's dependent type theory. The main "source" definitions, theorems and proofs in this repository are all taken from Scholze's Bonn lecture notes Analytic.pdf explaining some of his work with Clausen on the theory of solid and liquid modules, and on their development of a new approach to certain proofs in complex analytic geometry. #Liquid notes ilok pdfDigitisation, or formalisation, is a process where the source material, typically a mathematical textbook or a pdf file or website or video, is transformed into definitions in a target system consisting of a computer implementation of a logical theory (such as set theory or type theory). The main aim of this community-owned repository is to digitise some mathematical definitions, theorem statements and theorem proofs. For the eponymous blogpost by Peter Scholze which started it all: see. ![]()
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