chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
9,697 | lean_file_chunk | 1dd8d50fc0b32f862522583d5b1b68da479633ebe12adc6711b5ab5045752677 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Alexander Loitzl, Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Loitzl, Martin Dvorak
-/
import LeanPool.PumpingCfg.ChomskyNormalForm.Basic
import LeanPool.PumpingCfg.ToMathlib
/-!
# Parse trees for Chomsky normal form ... |
13,635 | lean_file_chunk | c38d01cbe58d4adbcbf100fe4d1b02b1c9f84e196cf4d71aecffa841c051fe33 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Alexander Loitzl, Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Loitzl, Martin Dvorak
-/
import LeanPool.PumpingCfg.ChomskyNormalForm.Translation
import LeanPool.PumpingCfg.Utils
import LeanPool.PumpingCfg.ParseTree
impo... |
1,075 | lean_file_chunk | 04d031029bdbb7df628814361d7cea461486d55329b785797244264354dd76b6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Alexander Loitzl, Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Loitzl, Martin Dvorak
-/
import LeanPool.PumpingCfg.ChomskyNormalForm.Basic
/-!
# Auxiliary grammar lemmas
Small facts about `ChomskyNormalFormRule.Rewrite... |
1,368 | lean_file_chunk | 1776d50a0b1e4d39ea1e2fd731181842e48fcde46599976f555b915fdc9632bf | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Alexander Loitzl, Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Loitzl, Martin Dvorak
-/
import Mathlib.Data.List.Basic
/-!
# List repetition utilities
Defines `nTimes` (notation `l ^+^ n`), the `n`-fold repetition of a... |
1,724 | lean_file_chunk | 5a884b66711e958e24b77c20c8ad5744c1101e6d2fe766003629b5cf61c48350 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Alexander Loitzl, Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Loitzl, Martin Dvorak
-/
import LeanPool.PumpingCfg.Pumping
/-!
# Pumping Lemma for Context-Free Grammars
Source: url:https://github.com/AlexLoitzl/pumping... |
5,136 | lean_file_chunk | 6a249d7ffbdb0faefa62342eb8d949422c26430a88047c9d318588c35e8bbbb1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import Mathlib.Algebra.MvPolynomial.Funext
import Mathlib.Algebra.MvPolynomial.Monad
import Mathlib.NumberTheory.PythagoreanTriples
import Mathlib.NumberTheory.SumFour... |
20,130 | lean_file_chunk | 9aca25e8521edd7c083ce9531c62466496d73327f994523ce02d34b120b39bd4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.Basic
/-! # Explanatory and cited source statements
This file records source-level material from Frisch--Vaserst... |
6,782 | lean_file_chunk | 25a9508583f1a1019674e4da451f72b5d67bd1e9ca73d7b211aa3eb3812aacb8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.SourceLemmas
/-! # Integer-valued parametrization of all Pythagorean triples
This file contains the explicit fou... |
1,737 | lean_file_chunk | bcaa3537965882d389d8bb549bb95404b44f5304f5b8819abf40e9471627036d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.Basic
import LeanPool.PythagoreanPolynomialParametrization.SourceLemmas
import LeanPool.PythagoreanPolynomialParam... |
4,887 | lean_file_chunk | 3cd597339b2f975df5137df12c76707ed934d09b74b646e104ad677a730b4ceb | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.Basic
/-! # Integer-coefficient obstruction
This file contains the paper's impossibility result for a single tri... |
19,494 | lean_file_chunk | 25ca86b1c4985b1b03cfc063f338613eafbc60291183d262475fef1fc4314fd3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.IntegerValued
/-! # Positive Pythagorean triples and 16-parameter variant
This file contains the positive-triple... |
9,924 | lean_file_chunk | c14c36ef9bb6cf408f79d883e220af37abb2ad8954bb41878dbc2146423800f3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.Basic
/-! # Source-level handoff lemmas
These declarations mirror the intermediate claims used in the paper's pr... |
563 | lean_file_chunk | 22ec30399ab6970bc82131523156d63983a2d8d5bf6aeb8576259833220c910c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
import LeanPool.PythagoreanPolynomialParametrization.Main
/-!
# Polynomial parametrizations of Pythagorean triples
Source: arxiv:0706.0290, doi:10.1016/j.jpaa.2007.0... |
7,048 | lean_file_chunk | e7703952eea48fd4da58ace55409eca2bbcb6242586e237699255534c28537ef | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Defs
import LeanPool.QuasiBorelSpaces.MeasureTheory.Pack
import Mathlib.MeasureTheory.Constr... |
1,569 | lean_file_chunk | 9497767e13381b8144a8407a290371c25a69633ed954bfcd169061d93f596fe9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Basic
import LeanPool.QuasiBorelSpaces.Defs
/-!
# LeanPool.QuasiBorelSpaces.Chain
Imported... |
4,058 | lean_file_chunk | b3294c697379586ade1bb871ca727a044481c811f86ca2c94101f3529cbf9026 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.OmegaHom
/-!
# LeanPool.QuasiBorelSpaces.Cont
Imported Lean Pool material for `LeanPool.Qu... |
4,797 | lean_file_chunk | d89dddc813526f93787935a255e3a076686a4016b23e28e4684d59c5f70edafd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import LeanPool.QuasiBorelSpaces.MeasureTheory.Cases
import Mathl... |
1,777 | lean_file_chunk | 35550eb170d0bfcac28a748c96de6cf6bf09de748204d51cff0eaba412d472be | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Real
import LeanPool.QuasiBorelS... |
2,284 | lean_file_chunk | b43d5fa155fad717970c83f166a67c881ec16e356352658c60f0437954ed57e7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Multiset
import Mathlib.SetTheory.Cardinal.Order
/-!
# LeanPool.QuasiBorelSpaces.Finset
Im... |
3,508 | lean_file_chunk | ce146e23d2dfd53bb2b49a0e7d96bb31ca34769a89d64f1524df4bef17e8ef67 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.OmegaQuasiBorelSpace
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Basic
import... |
12,723 | lean_file_chunk | 2431d9dcf163c3e77c855154979f7c3d502daba5f3f8229b0133557267d1c01f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Hom
import LeanPool.QuasiBorelSpaces.Nat
import LeanPool.QuasiBorelSpaces.Pi
import LeanPool... |
4,218 | lean_file_chunk | fe98cd3953b551aca774d7430ac09a43931d70f2cb1b73a531fa820844941f2f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Prod
import LeanPool.QuasiBorelSpaces.Defs
/-!
# Exponentials of Quasi-Borel Spaces
This ... |
2,248 | lean_file_chunk | b2fee85f4f6ec8ac9233387fda1732210b1e46996726e8771e0c84ea7d619b1e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Prop
import LeanPool.QuasiBorelSpaces.Sum
import Mathlib.MeasureTheory.Constructions.BorelSp... |
1,345 | lean_file_chunk | 2a33a17fd778dea6ae593408174254d2eb5df0f71a7d937cdb467d81e5d27404 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Basic
/-!
# LeanPool.QuasiBorelSpaces.Lift
Imported Lean Pool material for `LeanPool.Quasi... |
3,188 | lean_file_chunk | ed7b95110ac299cf17077450ef2223068573599be567010dd91408ef1c8583dc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.TypeStar
import Mathlib.Data.Nat.Notation
import Mathlib.Data.Fin.Basic
/-... |
12,505 | lean_file_chunk | c270b1fabea6fbcf6b6d4f62d491bed292b01082562e47384aae79dc69ed0d59 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Hom
import LeanPool.QuasiBorelSpaces.IsHomDiagonal
import LeanPool.QuasiBorelSpaces.List.Enc... |
1,927 | lean_file_chunk | 22e1f56f45db24dd826d8d41d570c9b7e52da7ba7f1c462d01fa7e8cda68959b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.MeasurableSpace.Constructions
/-!
# LeanPool.QuasiBorelSpaces.MeasureTheory.Cases
Imported Lea... |
507 | lean_file_chunk | 949c64dbb9da8560f7fc3eaa798586c14fa2b70ff2c785ddbc738a89b465890a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.MeasurableSpace.Defs
/-!
# LeanPool.QuasiBorelSpaces.MeasureTheory.Instances
Imported Lean Poo... |
3,959 | lean_file_chunk | 9171d6c49db51d0ef01f4a70597c9b31f198f6d600dedadc33fce42b8587d941 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Tactic.FunProp
import LeanPool.QuasiBorelSpaces.MeasureTheory.Sigma
import Mathlib.MeasureTheory.MeasurableSpa... |
3,913 | lean_file_chunk | 3de3f1fbecaace48fc63de910b32b5331b058541c0f5522af7ec24bb58f73a1d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Probability.Kernel.MeasurableLIntegral
import LeanPool.QuasiBorelSpaces.MeasureTheory.Option
import Mathlib.Pr... |
3,099 | lean_file_chunk | 1c7b0d5b501735ae4eac353e2e44a8b00d1245b49f7b03df1ea828cc2c53dbd5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.MeasureTheory.StandardBorelSpace
import Mathlib.MeasureTheory.Constructions.Polish.Basic
imp... |
2,003 | lean_file_chunk | 589fd743bf5bad9bf4c6d98c44371ccb8f211a676de09e9ca5163198ccc1e07c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal
import Mathlib.MeasureTheory.Constructions.Polish.Basic
/-!
... |
2,953 | lean_file_chunk | eaba32a2df76c808210b0c02e0579dc20a2aff0b72d59f1cddd15ec4d145d04d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Probability.Kernel.Composition.MeasureComp
import Mathlib.MeasureTheory.Constructions.UnitInterval
import Math... |
6,133 | lean_file_chunk | 9e474c97379bbc7f1794d62411895adc1f1c5a93d19c9165454ec27365e2d435 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Probability.CDF
import LeanPool.QuasiBorelSpaces.MeasureTheory.Measure
import Mathlib.MeasureTheory.Constructi... |
8,230 | lean_file_chunk | f290ad63988d05b4e8d5955b4a0503c4b29b2ba9f542c82874ad97e9404bc70b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Analysis.SpecialFunctions.Sigmoid
import LeanPool.QuasiBorelSpaces.MeasureTheory.Cases
import LeanPool.QuasiBo... |
5,457 | lean_file_chunk | 8368721c9c485523667736f4a4a6c85e3d5180987f0abf5b63f27a104a5ab8ac | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.MeasureTheory.Cases
import Mathlib.MeasureTheory.MeasurableSpace.Constructions
/-!
# LeanPo... |
2,078 | lean_file_chunk | ac39ee7d2334523a97106b545053c6b61335f77f7655e38f275ddaf45d1931f9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal
import Mathlib.MeasureTheory.Constructions.Polish.Basic
/-!
... |
4,264 | lean_file_chunk | 244d78a0c284c255d89ca35d5763d83a3a5ad160514e5293b465539f711f918a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Constructions.Polish.Basic
/-!
# LeanPool.QuasiBorelSpaces.MeasureTheory.Sum
Imported Lean Poo... |
1,119 | lean_file_chunk | 24a8dff49b445fd8de7705a5e15e17c0d274b315f902e35fd463626c14a6d57e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.MeasureTheory.Cases
import LeanPool.QuasiBorelSpaces.MeasureTheory.Instances
import LeanPool.... |
2,430 | lean_file_chunk | 153fee1fb15a408e83796889a943ffbdbb0e9e1f758e747020dfc50558dbf403 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.List
import LeanPool.QuasiBorelSpaces.Quotient
import LeanPool.QuasiBorelSpaces.IsHomDiagona... |
2,745 | lean_file_chunk | 4eaca00efa7598feee763bd5c4ff7565b084c7e372e6c0a3d0ac9475a3448f48 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Prod
import LeanPool.QuasiBorelSpaces.Prop
/-!
# LeanPool.QuasiBorelSpaces.Nat
Imported Le... |
4,044 | lean_file_chunk | 9f522537e8c826df455d95f7ace3af583c62b5f1bb69b17d16e5515bb35d2b6b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Integral.Lebesgue.Add
import Mathlib.Order.OmegaCompletePartialOrder
import LeanPool.QuasiBorelS... |
725 | lean_file_chunk | 9fd33db2716d335763cb0fbcd5c1e6027a360234f3011672a88f2a561d6c9a1e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Order.OmegaCompletePartialOrder
/-!
# LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Chain.Const
Import... |
4,309 | lean_file_chunk | 03d800a817bc77a704c3c763ad380d8c5a8d7c08054541ef76666a79a1028e79 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Option.Instances
import Mathlib.Data.Nat.Find
import Mathlib.Order.OmegaCompletePartialOrder... |
2,181 | lean_file_chunk | 625b14e6eef953b6a4082ae139de7c0a23583814b6fa1591cfbfd99821379a83 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.Sigma.Order
import Mathlib.Order.Defs.PartialOrder
import Mathlib.... |
3,731 | lean_file_chunk | 2559d52b4150671a31e09dba87eebb06dfb30ad0ac86da975ef43b4b654e260e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.Sum.Order
import Mathlib.Order.OmegaCompletePartialOrder
/-!
# C... |
655 | lean_file_chunk | 8c85bb3bfcb57b4d2c868cadee15bb22abf0c9877e728a3827a060ee0e995ae4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Chain.Const
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOr... |
2,188 | lean_file_chunk | 0d15a8edadfb5487a93ad463efd94472b8ed79ca1373e83eba2fc93e225c76a9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Order.OmegaCompletePartialOrder
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Basic
/-!
# LeanPo... |
6,734 | lean_file_chunk | ce5e81f00ee950ae07b67a44574606d17e847232958ff5cea865edc2703fb66e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Basic
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.C... |
1,405 | lean_file_chunk | ed8953e997751bce6a23baf106794afd05f5657a92c09475f763f03f1a1bf3e9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Data.Sigma.Order
import Mathlib.Order.OmegaCompletePartialOrder
import LeanPool.QuasiBorelSpaces.OmegaComplete... |
1,908 | lean_file_chunk | 664cab081684a842e911c08ec56420db4ae0ec842ab1c32c3d61b96a7531dd65 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Data.Sum.Order
import Mathlib.Order.OmegaCompletePartialOrder
import LeanPool.QuasiBorelSpaces.OmegaCompletePa... |
789 | lean_file_chunk | 0b9c7b6b7f3bcbae9538fe44ea9c03cff4f298bbfc643fce295f884e2ab4c8be | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Basic
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Ch... |
10,341 | lean_file_chunk | fa85f887b957f4f5d992dbd497384b206a9b32003667c1e226d9519143c1381e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Hom
import LeanPool.QuasiBorelSpaces.OmegaCompletePartialOrder.Basic
import LeanPool.QuasiBo... |
2,237 | lean_file_chunk | f31e11895edc6b902c5cbd128d4d82cee21c4e076b9c4abf3212bc5ff3b53964 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Order.OmegaCompletePartialOrder
import LeanPool.QuasiBorelSpaces.Basic
import LeanPool.QuasiBorelSpaces.Chain
... |
1,597 | lean_file_chunk | b8e8f598d795375099ff01697b3e5c6e8f9049111783283e682f78d831294179 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Data.Option.Basic
import Mathlib.Order.BoundedOrder.Basic
import Mathlib.Order.Defs.PartialOrder
/-!
# LeanPo... |
5,454 | lean_file_chunk | 4a8105669e60f0d51c65f90efe55f117d714dda5bff81c3d247043e4622de76c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.IsHomDiagonal
import LeanPool.QuasiBorelSpaces.Nat
import LeanPool.QuasiBorelSpaces.OmegaCom... |
2,481 | lean_file_chunk | b09792de9c87c425a9b4420374076e2671c8598dd6c449f30da2c64460f4b502 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Prod
import LeanPool.QuasiBorelSpaces.Defs
import LeanPool.QuasiBorelSpaces.OmegaQuasiBorelS... |
22,211 | lean_file_chunk | 99a23a6db39ec56a76298db9aac335eaa39375c04ec464bfb22d38365eb5f2db | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Constructions.UnitInterval
import Mathlib.MeasureTheory.Measure.DiracProba
import LeanPool.Quasi... |
23,608 | lean_file_chunk | b18b692750904af141dc7a646111fa67054b23bf80c7cd0083f0464abdef1066 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.ENNReal
import LeanPool.QuasiBorelSpaces.PreProbabilityMeasure
import LeanPool.QuasiBorelSpa... |
4,360 | lean_file_chunk | 32fc16991300aeebbaee6e4f172a4d0fc2a3180b3378644de7ed216e8ec67447 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.MeasureTheory.Measure.Prod
import LeanPool.QuasiBorelSpaces.Basic
import Mathlib.MeasureTheory.Integral.Lebesg... |
4,316 | lean_file_chunk | 9d360363ca434d01ecc9788748541e846e7b926eb7cf958394ed19e80c9d4b7f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Basic
import LeanPool.QuasiBorelSpaces.Pi
import LeanPool.QuasiBorelSpaces.Defs
import LeanP... |
2,508 | lean_file_chunk | 75d6ca07a7b6440d1e2b43806e17a1e3be550dd1a94039cc9b6baf8cec3206c8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Hom
import LeanPool.QuasiBorelSpaces.Prod
import LeanPool.QuasiBorelSpaces.Defs
/-!
# LeanP... |
2,248 | lean_file_chunk | bc2919dde3a3a1ca589107a35cc4e17587744738c62d5339f2ead57be759f062 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.RoseTree.Defs
import LeanPool.QuasiBorelSpaces.RoseTree.Basic
/-!
# LeanPool.QuasiBorelSpac... |
9,536 | lean_file_chunk | 501eabc96464948d823fc38369998aacbfe6e34ae68cb88bfb697c12bbd36f05 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Hom
import LeanPool.QuasiBorelSpaces.Rose.Encoding
import LeanPool.QuasiBorelSpaces.List
imp... |
9,373 | lean_file_chunk | 1a84714f374160e807a17096fad043b228db05e4ec6e2e59ef1999fa44825718 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.RoseTree.Defs
import Mathlib.Tactic.NthRewrite
import Mathlib.Control.Traversable.Instances
... |
3,058 | lean_file_chunk | 726e9d4fa9580794d59ac29617a343fa073a1a49f951d00ff3558dafc80ef010 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.TypeStar
import Mathlib.Logic.Equiv.List
import Mathlib.Logic.Encodable.Bas... |
495 | lean_file_chunk | d1946b2bad06e7f941bcd8b94f6162587270331b1d515410a124e61d4f0fe70f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.RoseTree.Basic
import LeanPool.QuasiBorelSpaces.RoseTree.Defs
/-!
# Rose trees (vendored)
V... |
4,072 | lean_file_chunk | 5787f3b41163e4730045206c9ff91507f55cd99a4b092c4d6c47e9555a1f891b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Prop
import LeanPool.QuasiBorelSpaces.Sigma
import LeanPool.QuasiBorelSpaces.Sum
/-!
# Lean... |
16,919 | lean_file_chunk | f843fd34ecf2f3b29eee4152679aad6f97d0e6290f6739c38b56bc1fe54e55c9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.MeasureTheory.Cases
import LeanPool.QuasiBorelSpaces.MeasureTheory.Sigma
import LeanPool.Qua... |
2,177 | lean_file_chunk | 3fc5118b6f0140c677dc808e543cbbc6045cbfd4192ad52871dc02765a10b72e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Basic
import LeanPool.QuasiBorelSpaces.Defs
import LeanPool.QuasiBorelSpaces.OmegaQuasiBorel... |
5,471 | lean_file_chunk | a8dfa2e3a432464c1ce12e4f39020020741dc505de080997bdc390c7379066b7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Hom
import LeanPool.QuasiBorelSpaces.Lift
import LeanPool.QuasiBorelSpaces.OmegaCompletePart... |
3,226 | lean_file_chunk | 15f78356c8bcb11a2f7073b0b7841deca4b08f448ef2d32584f357ffb4ff07ce | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import Mathlib.Topology.UnitInterval
/-!
# LeanPool.QuasiBorelSpaces.UnitInterval.AssocProd
Imported Lean Pool material for... |
369 | lean_file_chunk | 7bfac0b96cc25e269ae11fc361735c8a4d9ca42812f6d2789d3d1a54deaa4f18 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.UnitInterval.AssocProd
/-!
# Unit interval modules
Re-exports the `UnitInterval` sub-module... |
2,804 | lean_file_chunk | 43b069a85468e2bd1047e4d455b5f3858ed2549a848bf5333144f62077daaeab | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Anthony Vandikas, Kiarash Sotoudeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Vandikas, Kiarash Sotoudeh
-/
import LeanPool.QuasiBorelSpaces.Basic
import LeanPool.QuasiBorelSpaces.Chain
import LeanPool.QuasiBorelSpaces.Cont
import Le... |
23,965 | lean_file_chunk | f0866b7e8b78f9953417929c4c4f6910151504a143573faf3ef191137ec427d4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Barinder S. Banwait. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Barinder S. Banwait, Xinze Li
-/
import LeanPool.RamanujanNagell.Helpers
/-!
# The Ramanujan-Nagell equation
The integer ring `R = ℤ[(1 + √-7)/2] = QuadraticAlgebra ℤ (-2) 1` i... |
23,982 | lean_file_chunk | 81e4379c1b29414a2a1b2a8ddec4e5ce7d125af6dae7ab3a30548a5c143c22ca | lean_source_file | lean_pool_source_file_chunks | exact dvd_add h_div (dvd_trans (pow_dvd_pow 7 (by omega : l ≤ l + 1)) h_tail)
· intro h_contra
apply h_ndiv
rw [h_split, h_f0] at h_contra
have := dvd_sub h_contra h_tail
simpa using this
/-- A'_d = Σ_{j=0}^{d/2-1} C(d, 2(j+1)) · (-7)^j. -/
noncomputable def binomialA' (d : ℕ) : ℤ :=
∑ j ∈ Finset.r... |
535 | lean_file_chunk | 4310abdf0c348d275310af99eccef345e3cac2064b6d2eb84cf96c5817507237 | lean_source_file | lean_pool_source_file_chunks | `(±5, 5)`, `(±11, 7)`, and `(±181, 15)`. -/
theorem ramanujanNagellExact :
∀ x : ℤ, ∀ n : ℕ, x ^ 2 + 7 = 2 ^ n ↔
(x, n) = (1, 3) ∨ (x, n) = (-1, 3)
∨ (x, n) = (3, 4) ∨ (x, n) = (-3, 4)
∨ (x, n) = (5, 5) ∨ (x, n) = (-5, 5)
∨ (x, n) = (11, 7) ∨ (x, n) = (-11, 7)
∨ (x, n) = (181, 15) ∨ (x, n) = (-181, 15) :=... |
18,929 | lean_file_chunk | 30883667fa943b30428f52380080a8f18890486bbdff92b2fc60a6dc27393f66 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Barinder S. Banwait. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Barinder S. Banwait
-/
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.QuadraticAlgebra.NormDeterminant
import Mathlib.Algebra.Order.Round
import Mathlib.Dat... |
1,603 | lean_file_chunk | 6dc8a7650ed6aad96835100888d1520bddffbdc435d562508009b5002b999e16 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Barinder S. Banwait. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Barinder S. Banwait, Xinze Li
-/
import LeanPool.RamanujanNagell.Basic
import LeanPool.RamanujanNagell.Helpers
/-!
# The Ramanujan-Nagell theorem
Source: arxiv:2604.09808
Autho... |
23,983 | lean_file_chunk | f48bbe87d11f43fb944522acd37ff2bdc5be0454e98d4995bcfaf1dde5d47d70 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
import Mathlib.Analysis.SpecialFunctions.Log.Basic
... |
23,979 | lean_file_chunk | a19a14f2f88a159b19f70eef5e5475c60720ce28013a75a7851e7e78d4ac40ff | lean_source_file | lean_pool_source_file_chunks | have hX_X2 : X₂ < X :=
lt_of_le_of_lt (le_max_right X₁ X₂ |>.trans (le_max_left _ X₃)) hX_maxL
have hX_X3 : X₃ < X := lt_of_le_of_lt (le_max_right _ X₃) hX_maxL
have hX_pos : (0 : ℝ) < X := by linarith
set K := ⌊Real.log X / (2 * Real.log 2)⌋₊ with hK_def
have hK3 : 3 ≤ K := floor_log_ge_three X hX64
have... |
23,946 | lean_file_chunk | f117fd117fb0013d0fb7efe550967c7606d17aa95f71b6dcd73bf634b4e7a9f7 | lean_source_file | lean_pool_source_file_chunks | rw [show n = 0 by rwa [pow_eq_zero_iff hk.ne'] at hnk]
· simp only [hm, ↓reduceIte]
exact Finset.prod_primes_dvd n
(fun p hp => (Nat.mem_primeFactors.mp hp).1.prime)
(fun p hp => prime_factor_dvd_of_dvd_pow m n k hk h p hp)
lemma gcd_quotients_coprime (M N : ℕ) (hM : 0 < M) (_hN : 0 < N) :
let g ... |
23,994 | lean_file_chunk | e39bd2a37a386c01f44f788f17fe0ffd3f5057d8a541b42c38b7648363b6f7e2 | lean_source_file | lean_pool_source_file_chunks | rcases le_or_gt (y ^ 2) ((x : ℤ) ^ 11) with hge | hlt
· exact E2_abc_case_A K hK x hx y hy d hd hd_eq h1 hge
· exact E2_abc_case_B K hK x hx y hy d hd hd_eq h2 hlt
lemma E2_abc_applied (K : ℝ) (hK : 0 < K)
(hK_abc : ∀ a b c : ℕ, 0 < a → 0 < b → 0 < c →
Nat.Coprime a b → a + b = c →
(c : ℝ) ≤ ... |
23,993 | lean_file_chunk | d6100a98dcd041b5a244c555eb007b2f76ece5569091a265210cbf9751da1536 | lean_source_file | lean_pool_source_file_chunks | pnat_bounded_finite B
lemma pnat_bounded_finite_nat (M : ℕ) :
{p : ℕ+ | (p : ℕ) ≤ M}.Finite := by
apply Set.Finite.subset (pnat_bounded_finite_k1 (M : ℝ))
intro p hp
simp only [Set.mem_ofPred_eq] at hp ⊢
exact_mod_cast hp
lemma witness_set_subset_bounded (X : ℝ) :
{p : ℕ+ | (p : ℕ).Prime ∧ (p : ℝ) ≤ X... |
23,952 | lean_file_chunk | 10fe07e072066961fe627ed7d079c3954c0e43a02a179281787506993db6e01a | lean_source_file | lean_pool_source_file_chunks | have h₄ : -|(u ^ 2 - 5 * (↑(x : ℕ) : ℤ) ^ 22 : ℝ)|
≤ (u ^ 2 - 5 * (↑(x : ℕ) : ℤ) ^ 22 : ℝ) := neg_abs_le _
linarith
exact h₃
linarith
lemma u_sq_in_interval (X : ℝ) (x : ℕ+) (u : ℤ)
(h : (|u ^ 2 - 5 * (↑x : ℤ) ^ 22| : ℝ) ≤ 4 * X) :
5 * (↑↑x : ℝ) ^ 22 - 4 * X ≤ (↑u : ℝ) ^ 2 ∧
(↑u : ℝ) ... |
23,976 | lean_file_chunk | 9c413a4cb0e67639c4ec238621e696c833f5e8237318586e35b997429314f084 | lean_source_file | lean_pool_source_file_chunks | lemma abc_E4_case_pos (K : ℝ) (hK : 0 < K)
(ε : ℝ) (hε : 0 < ε)
(habc_ineq : ∀ a b c : ℕ, 0 < a → 0 < b → 0 < c →
Nat.Coprime a b → a + b = c →
(c : ℝ) ≤ K * ((Nat.radical (a * b * c) : ℕ) : ℝ) ^ (1 + ε))
(x : ℕ+) (u : ℤ)
(hu_ne : u ≠ 0)
(hD_pos : u ^ 2 - 5 * (↑(x : ℕ) : ℤ) ^ 22 > 0) :... |
23,981 | lean_file_chunk | 875015c16c73af186f1bdd35ab73e9dd1276bccb439df60ded44448cdc764c42 | lean_source_file | lean_pool_source_file_chunks | exact abs_four_mul_tau_ge_one R p ℓ hℓ_prime hℓ_eq
· have hid_abs : |(2 * R.τ p ^ 2 - 3 * (↑↑p : ℤ) ^ 11) ^ 2 - 5 * (↑↑p : ℤ) ^ 22| =
|4 * R.τ (p ^ 4)| := congrArg (|·|) hid
exact witness_in_E4_set_upper R X p hp ℓ hℓ_le hℓ_eq hid_abs
open Classical in
private noncomputable def witnessP (R : RamanujanTau... |
23,991 | lean_file_chunk | 451ae72456e4faf4541535c6415dd50a17d3397145781105da8c1c7f582c9d22 | lean_source_file | lean_pool_source_file_chunks | lemma caseB_lower_bound_cast_ineq (x : ℕ+) (y : ℤ)
(h : (↑↑x : ℤ) ^ 11 + 1 ≤ y ^ 2) :
(↑↑x : ℝ) ^ 11 + 1 ≤ (y.natAbs : ℝ) ^ 2 := by
rw [natAbs_sq_real]
exact_mod_cast h
lemma caseB_lower_bound (x : ℕ+) (y : ℤ)
(hy_lower : (↑↑x : ℤ) ^ 11 + 1 ≤ y ^ 2) :
Real.sqrt ((↑↑x : ℝ) ^ 11 + 1) ≤ (y.natAbs : ℝ)... |
22,304 | lean_file_chunk | fb82c50002b803ffb6162d0a2af1c5ee621433120c2568cef7f95ff7d74faa9b | lean_source_file | lean_pool_source_file_chunks | lemma pnat_bounded_finite (B : ℝ) (_hB : 0 < B) :
{x : ℕ+ | (x : ℝ) ≤ B}.Finite :=
_root_.pnat_bounded_finite B
lemma y_sq_le_real_of_E2_cond (x : ℕ+) (y : ℤ) (X : ℝ)
(h2 : (|(↑↑x : ℤ) ^ 11 - y ^ 2| : ℝ) ≤ X) :
(y : ℝ) ^ 2 ≤ (↑↑x : ℝ) ^ 11 + X := by
rw [show (|(↑↑x : ℤ) ^ 11 - y ^ 2| : ℝ) = (|(↑↑x : ℝ)... |
1,961 | lean_file_chunk | d760155af8d4b08412b468cab1108627812425509e03eba689a622f275ced064 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import LeanPool.RamanujanTauMissesPrimes.Solution
/-!
# ABC implies that Ramanujan's tau function misses a... |
10,310 | lean_file_chunk | 95ad410f8fc9dddb623af6cc304d55a908380cfe3a859eae0c2968ba2931d5fb | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.RingTheory.Radical.NatInt
import LeanPool.Redhill.Common.Conjectures
/-!
# Browkin and Brzeziński's 1994 re... |
4,283 | lean_file_chunk | 259a9ab2078fb39a6f2cdc43b9d61f85ab6d06a8622be4d605c6c0d5eb79dbb0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import LeanPool.Redhill.Common.PairwiseCoprime
import LeanPool.Redhill.Common.Quality
import LeanPool.Redhill.Common.SubsumCondition
/-!
# Definitions of the tuple sets and... |
1,053 | lean_file_chunk | 9e26906c7a72800d8855a9670ae254718c0428f1da51837c4e76ae54b863b467 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Data.Fintype.Basic
/-!
# Maximum absolute value of a tuple of integers
-/
open Finset
variable {n : ℕ}
/-- The ma... |
894 | lean_file_chunk | 616b5d316f4dd8dab86434f943aa2b0dcfa92bb1260642811785a7e39cedd765 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Algebra.GCDMonoid.Finset
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# Pairwise coprimality
-/
/-- A predicate stating that the given tuple's numbers are ... |
6,262 | lean_file_chunk | 207049dc19df445a6e2c474b0303beb49781d0cb5da08522704ea8198994e068 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Data.Nat.Prime.Infinite
import LeanPool.Redhill.Common.SubsumCondition
/-!
# Prime chains
These are sequences of primes where the next prime is at least twi... |
2,695 | lean_file_chunk | 555c5caae982b399ad0c4a8d67c753c0c82efb207179e3c434b204ad4a932315 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Algebra.EuclideanDomain.Int
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.RingTheory.Radica... |
9,359 | lean_file_chunk | 8783e95ea7c1d398921692acd3e1bdbf24a35fa6f0ab131140695b66e4da2f06 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Sign.Defs
/-!
# Subsum co... |
10,488 | lean_file_chunk | fb96ab47cd59e442710f53de75bd1e374711b7bd20216eb87c2954d6a155a8b1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Data.Nat.ChineseRemainder
import Mathlib.Data.Nat.Factors
import Mathlib.Data.ZMod.Defs
import LeanPool.Redhill.Common.PrimeChain
/-!
# VW pairs
The paper s... |
18,200 | lean_file_chunk | 0f1c81fc012d79a993a2630b3ee89c1730cc7075f69edefdd6d58620cd3bf884 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Order.Filter.Finite
import LeanPool.Redhill.Common.PairwiseCoprime
import LeanPool.Redhill.General.Defs
/-!
# Coprimality proof for the general case
In the ... |
6,241 | lean_file_chunk | ddb608227e817aa53a5f43611d701b3b589f6053251d67747c2106aa63cc29c9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.FieldTheory.Finite.Basic
import LeanPool.Redhill.Common.VWPair
/-!
# Definitions for the general case
In this section `h` is the variable such that `tup n F... |
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