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 |
|---|---|---|---|---|---|
4,922 | lean_file_chunk | ccc34db4c8c45f751db699701992f4b91f9ac08dc4b3f3e4a2e0dfb28dfb2f1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Disintegration.CondCDF
/-!
# Cumulative distribution function of a real probability measure
The cumulative distribution... |
2,998 | lean_file_chunk | c7fd8b0dbcae70bc55ae5dfe4148170b723c59884d634fdd16d86895edc538dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
module
public import Mathlib.Probability.Notation
public import Mathlib.Probability.Independence.Basic
public import Mathlib.MeasureTheory.Function.ConditionalExpectation.... |
4,969 | lean_file_chunk | e575d4f647af43cd9bda556360a1d8d4ddf2c0af3fa36384cc764c87689172e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
module
public import Mathlib.Init
/-!
Defines a command wrapper that prints the changes the command makes to the
environment.
```
whatsnew in
theorem foo : 4... |
3,195 | lean_file_chunk | b4da151d4940a4ea1835002c84802cfe769c0e9b6b8d08b1f35665b67b7b0667 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public meta import Mathlib.Data.String.Defs
public import Mathlib.Init
/-!
# Format Table
This file provides a simple function for formatting a two-dimensiona... |
3,022 | lean_file_chunk | 12e8fa61d10223ea50938099bccf26761bcbffb8d2ccf50923bbff6cd7eb015a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Gabriel Ebner, Yuyang Zhao
-/
module
public meta import Lean.Meta.Tactic.Delta
public import Mathlib.Init
/-!
# Term elaborators for reduction
-/
public meta section
name... |
2,678 | lean_file_chunk | fd8dfd77be91c0919780b472caa6d7874705e9a9c3119f3c0fcc53e775fb3401 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Matthew Robert Ballard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matthew Robert Ballard, Damiano Testa
-/
module
public meta import Lean.Elab.Command
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header ... |
3,189 | lean_file_chunk | c2155a6c3e9a7a4467f6c305c5e0c05e575f606465782584ef630d77df9061a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Alex J. Best, Yaël Dillies
-/
module
public import Mathlib.Init
public import Qq
public import Qq.Typ
/-!
# Extra `Qq` helpers
This file contains some additional functio... |
1,911 | lean_file_chunk | dff11ca5998b3888061b1a15ed00d7229c4df34bb854e5e284586270563d2f1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Init
/-! # The `#trans_imports` command
`#trans_imports` reports how many transitive imports the current module has.
The command takes a... |
6,444 | lean_file_chunk | 49a9be93d0b15165ca567a8690ed2b5b1d31da309c3b681492219622f3e0fc88 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Henrik Böving, Yaël Dillies, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving, Yaël Dillies, Kyle Miller
-/
module
public meta import Mathlib.Lean.Expr.Basic
public meta import Lean.Elab.Command
public import Lean.Meta.So... |
23,978 | lean_file_chunk | 79fa5c7c594aae530a78237ebdd11dc9f2d88324be1ebac7ec3c0f8d55b8a9ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kyle Miller
-/
module
public meta import Lean.Elab.MacroArgUtil
public meta import Lean.PrettyPrinter.Delaborator -- shake: keep (dependency of elaborator outp... |
7,665 | lean_file_chunk | e6dd703a978f100bcaaecaf9e90d11a055888514178faac74c0a2bc4d2d1bebf | lean_source_file | pkg_mathlib_source_file_chunks | -- Arguments for the LHS pattern in the `macro`. Also used to construct the syntax
-- when delaborating
let mut pattArgs := #[]
-- The matchers to assemble into a delaborator
let mut matchers := #[]
-- Whether we've seen a `(...)` item
let mut hasBindersItem := false
-- Whether we've seen a `scoped` item
... |
6,465 | lean_file_chunk | 39287855378fde85238a0a89475e0c684386bf0087ce64ed51ed71ed249b07c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth
-/
module
public import Mathlib.Init
public meta import Lean.Elab.Tactic.Location
public meta import Lean.Meta.Tactic.Simp.Main
public import Lean.Elab... |
815 | lean_file_chunk | 2c3ec188fd140980e050b55b5cbdd9270fde1a0a853aec0eb72e392ae5e7051b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Init
/-!
Mathlib-specific pretty printer options.
-/
public meta section
namespace Mathlib
open Lean
/--
The `pp.mathlib.binderPredicates... |
2,277 | lean_file_chunk | e810efa9b9d35cb612ed6e16b55f66611bc691e1bad26c90136c30ae0d13da1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kim Morrison, Damiano Testa
-/
module
public import Mathlib.Init
public meta import Lean.Util.Path
/-!
# Utility functions for finding all `.lean` files or modules in ... |
5,069 | lean_file_chunk | 201a5549806ef9a8e4983930e0845ae1f3863ff349bbd3bcaf9a760195c24f1b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Init
public meta import Lean.Meta.Tactic.Simp.Types
public import Qq
public import Qq.Typ
/-!
# A monad for tracking and deduplicating ... |
1,432 | lean_file_chunk | bbc2314a61b5ce64a3b70921368a8085261a5ae6ebbd59b5f47b84dbfd9c9569 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best
-/
module
public import Mathlib.Init
public meta import Lean.Elab.Tactic.Basic
/-!
# Defines `sleep_heartbeats` tactic.
This is useful for testing / debugging long runnin... |
1,397 | lean_file_chunk | ea13fa9ee621550646321a38cd09fe895fb6b7bbafcbc16c0d453754063b324f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Daniel Selsam, Gabriel Ebner
-/
module
public import Mathlib.Init
/-!
# Defines `with_weak_namespace` command.
Changes the current namespace without causing s... |
11,097 | lean_file_chunk | 538ab8602a1f2beffddcb59e3d5c21faa767cd5c5928a08b3572d5f0ece3fff4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Init
public meta import Lean.Util.Heartbeats
public meta import Lean.Meta.Tactic.TryThis
/-!
Defines a command wrapper that prints the numb... |
14,047 | lean_file_chunk | c2d4100baead16bc7284c58fa5afe57afa170670d9303aa9b47bf8f59a19fdd1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Init
/-!
# A parser for superscripts and subscripts
This is intended for use in local notations. Basic usage is:
```
local syntax:arg ... |
7,430 | lean_file_chunk | 4cb9f9ffad465c501950f2effa9fe8c86fbdd5355a62b52aec04929925f440c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Init
public meta import Lean.PrettyPrinter.Delaborator.Builtins
public import Mathlib.Util.PPOptions
/-! # Pi type notation
Provides the `Π ... |
844 | lean_file_chunk | 80d4ae61b591cdfd2bec262b00e94b45ff3129559c3b50f57f58e355cc69d510 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau
-/
module
public meta import Lean.Meta.Tactic.Simp.Types
public import Mathlib.Init
public import Qq
/-! # Additional simp utilities
This file adds additional tools for met... |
2,854 | lean_file_chunk | 8793f9c49028a595104ae7fb071792ad8a99d79f01a9329c1b7d8d2ef3c80342 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Jannis Limperg
-/
module
public import Mathlib.Init
public meta import Lean.MetavarContext
/-!
# Miscellaneous helper functions for tactics.
TODO: Ideally we would f... |
11,371 | lean_file_chunk | c4e12d73afc3e2ceb3c22edb2fc672e1541f7e2f9fd2e2929e72deef5e0e5f32 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Parth Shastri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parth Shastri, Gabriel Ebner, Mario Carneiro
-/
module -- shake: keep-downstream (`[csimp]` is not currently tracked)
public import Mathlib.Init
public meta import Lean.Elab.Command
p... |
629 | lean_file_chunk | 0ab40841b175ae918054e6802c132c082a76694dab04556e00ed2f8e532ef3e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Vasilii Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasilii Nesterov
-/
module
public import Mathlib.Init
/-!
# `elabTermWithoutNewMVars`
-/
public meta section
open Lean Elab Tactic
/-- Elaborates a term with `errToSorry = fals... |
1,113 | lean_file_chunk | 66b1f696d1d1a1627cbefb0dff447b012c0f8284a2903a40729abc37627a29c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best
-/
module
public import Mathlib.Init
public import Batteries.Tactic.Exact
public import Lean.Meta.Tactic.Simp
/-!
## Dischargers for `simp` to tactics
This file defines a... |
6,942 | lean_file_chunk | 571d6e94d7c59507052c0c632f21fcfb94bb81b7b2900343e095402f45102c08 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Init
public meta import Lean.CoreM
public meta import Lean.Util.FoldConsts
/-!
A rudimentary export format, adapted from
<https:... |
714 | lean_file_chunk | 3c4c93189faac05f5379e58612c17d1889d439bf6089d2765e3d21d764bfec25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
module
public import Mathlib.Init
public meta import Lean.Util.CollectAxioms
public meta import Lean.Elab.Command
/-!
# Defines the `assert_no_sorry` command.
Throws... |
1,856 | lean_file_chunk | 997ab84a850529c3338b20883d7cfece213094e0c1249b1c01d31d801e22081a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public meta import Mathlib.Lean.Name
public meta import Mathlib.Lean.Expr.Basic
public meta import Lean.Elab.Command
public import Mathlib.Init
/-!
# Commands `#... |
2,164 | lean_file_chunk | 537eaecef1d3014b7bacfa3a04a0f2e896cd0d1013bf0c077c0247b787aee8e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public meta import Mathlib.Lean.Expr.Basic
public import Batteries.Tactic.Alias
public import Lean.Exception
/-! ## The `@[alias_in]` attribute -/
publi... |
3,210 | lean_file_chunk | 902fcf9be66b2f628a8f5e24e00a7d58da0a9da4d8e69624404d3ffb2fbeaee0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Init
public meta import Lean.Elab.Tactic.Basic
public import Qq
public import Qq.Typ
/-!
# `SynthesizeUsing`
This is a slight simplificati... |
3,898 | lean_file_chunk | 72533a8cbd016e200bd5f31991a26ba80ef07ee8fa390f9933dd977a79c0999c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.Init
public meta import Lean.Elab.DeclarationRange
/-!
# `addRelatedDecl`
-/
public meta section
open Lean Meta Elab
... |
1,315 | lean_file_chunk | c85203339c12f94376d7823b93df82f8e10424177ec1277830d29385af3b5443 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Edward Ayers
-/
module
public import Std.Data.HashMap.Basic
public import Mathlib.Init
/-!
# Fixpoint function with memoisation
-/
variable {α β : Type}
@[noinline, ... |
7,243 | lean_file_chunk | 1d74cdd8669dd0a12bd65388774bb475cfc5a3008ae9e320c364f8c2669e343b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.SpecificLimits.Normed
public import Mathlib.NumberTheory.ArithmeticFunction.Misc
/-!
# Lemmas on infinite sums over the antid... |
8,418 | lean_file_chunk | 04a872d92b81b052b507602ba1441b5fbf5ba31e1715567e8da8e3743a058a69 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg, Snir Broshi
-/
module
public import Mathlib.Analysis.Complex.IsIntegral
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
public import Mathlib.RingTheor... |
12,507 | lean_file_chunk | 3a1eea0ca49098f8d37af827f335f58652df2af17e4fc048149b22eccb8153df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, David Loeffler
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Derivative
public import Mathlib.Data.Nat.Cho... |
11,541 | lean_file_chunk | 6754589a44dc5d5a3fc4f6882e8e3327b5cfe8eacd22a466c6e4f0b3956255f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Bolton Bailey
-/
module
public import Mathlib.Data.Nat.Choose.Factorization
public import Mathlib.NumberTheory.Primorial
public import Mathlib.Analysis.Convex.Specif... |
7,742 | lean_file_chunk | f70c3c5d25d315754406e0f2ea806e749b9cb206bd387eb2ca2c4e6854bedeec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero, Laura Capuano, Amos Turchet
-/
module
public import Mathlib.Analysis.Matrix.Normed
public import Mathlib.Data.Pi.Interval
public import Mathlib.Tactic.Rify
publi... |
21,255 | lean_file_chunk | f494d693c9418ea7a9b9f7d2e0ab66b7b54f993044f0089b0d4e4a7acc2afa56 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.BernoulliPolynomials
public import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
public import Mathlib.Analysis.Cal... |
4,924 | lean_file_chunk | dae84d5ea6bd236e4d1e07d9fc72f60810438f7ce51e98fa1e7194de095b1fc8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Algebra.Order.Group.Indicator
public import Mathlib.Analysis.PSeries
public import Mathlib.NumberTheory.SmoothNumbers
/-!
# The sum of th... |
23,952 | lean_file_chunk | f4ffa862c5aa9397668f9fdfde227717dea4af544bfc7f530eda6668bcf05849 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Fin.Fin2
public import Mathlib.Data.PFun
public import Mathlib.Data.Vector3
public import Mathlib.NumberTheory.PellMatiyasevic
/-!... |
4,007 | lean_file_chunk | 8f24fcbbaacb06ed2fac5209675affe05a692798bebef7d9e0bba354e1e7191b | lean_source_file | pkg_mathlib_source_file_chunks | /-- Diophantine functions are closed under integer division. -/
theorem div_dioph : DiophFn fun v => f v / g v :=
have :
Dioph fun v : Vector3 ℕ 3 =>
v &2 = 0 ∧ v &0 = 0 ∨ v &0 * v &2 ≤ v &1 ∧ v &1 < (v &0 + 1) * v &2 :=
(D&2 D= D.0 D∧ D&0 D= D.0) D∨ D&0 D* D&2 D≤ D&1 D∧ D&1 D< (D&0 D+ D.1) D* D&2
dio... |
23,990 | lean_file_chunk | da6e9d9b8e9d658c7e464a91e804d8296a1183639177bd0f10179e6f8970bf32 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Geißer, Michael Stoll
-/
module
public import Mathlib.Data.ZMod.Basic
public import Mathlib.NumberTheory.DiophantineApproximation.Basic
public import Mathlib.NumberTheory.Zsqrt... |
4,082 | lean_file_chunk | 6527ffd74a91540f06b550140c869e20565c8f8dc9c273b6cef659ba86c4e3ad | lean_source_file | pkg_mathlib_source_file_chunks | _ ≤ d * a.y ^ 2 := (mul_le_mul_iff_left₀ <| sq_pos_of_pos hay).mpr h.d_pos
_ < d * a.y ^ 2 + 1 := lt_add_one _
_ = (1 + d * a.y ^ 2) * 1 := by rw [add_comm, mul_one]
_ ≤ (1 + d * a.y ^ 2) * a₁.y ^ 2 :=
(mul_le_mul_iff_right₀ (by have := h.d_pos; positivity)).mpr (sq_pos_of_pos h.2.1)
/-- Any nonnegat... |
2,659 | lean_file_chunk | dc15c81e8c14fbb94d570ddf5882d121de4960c7d7a28c72e3431d2e469e4a70 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Combinatorics.SetFamily.FourFunctions
public import Mathlib.Data.Nat.Squarefree
/-!
# The Marica-Schönheim special case of Graham's conject... |
10,679 | lean_file_chunk | cae11f6512797b3b908a1ec5416b04698e986be5cb79b6e697ec406dae351511 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Michael Stoll
-/
module
public import Mathlib.Data.Nat.Squarefree
public import Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity
public import Mathlib.NumberTheory.Padics.... |
16,863 | lean_file_chunk | 2efc31b7c07b18924b558bc050647eaa283aaf7111963272bcd2eb77f7663698 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kevin Buzzard
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.RingTheory.PowerSeries.Inverse
public import Mathlib.RingTheory.PowerSer... |
8,457 | lean_file_chunk | a6e0420778c5cb01f050e2b98ac45f203e5387577b1800a792c4b2144acff7bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jason Yuen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jason Yuen
-/
module
public import Mathlib.Data.Real.ConjExponents
public import Mathlib.NumberTheory.Real.Irrational
/-!
# Rayleigh's theorem on Beatty sequences
This file proves Rayle... |
10,104 | lean_file_chunk | 2d55d450348dcbe3e8de4a340cd9ebfdf58e25ff68b93aa98ad6fdcfbddf4b88 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.FieldTheory.Finite.Basic
/-!
# Lagrange's four square theorem
The main result in this file is `sum_four_squares`,
a proof that every natur... |
23,984 | lean_file_chunk | 84eadd9264be1167d49c20fb8b33619858ce1d6c80af975e5e2e604911d52e12 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Lin... |
22,306 | lean_file_chunk | 7c2064da289ff6ffb8abec64ee84667520df10ea562cbb5b19a6d4f952aeef41 | lean_source_file | pkg_mathlib_source_file_chunks | simp only [coe_mul, coe_S, coe_T_zpow, Matrix.mul_fin_two, mul_zero, mul_one, zero_add,
one_mul, add_zero, zero_mul]
fin_cases i <;> fin_cases j <;> tauto
rw [hg', mul_smul] at hg
have hSre : re (S • z) = -z.re := by
rw [modular_S_smul, ← coe_re, coe_mk, inv_re, normSq_eq_norm_sq, norm_neg, hz', one_p... |
186 | lean_file_chunk | 9755745ecacefca5ed400923b5e6d56e0747608a756e1e0e8a34fc87eaf4b2d7 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import Mathlib.NumberTheory.ArithmeticFunction.Misc
deprecated_module (since := "2025-12-02") |
2,917 | lean_file_chunk | f9f9a474f10cf48e8d2fe100ba94697d6aed98e77a28a34fd92e56cbe8dcfe74 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.RingTheory.Polynomial.Cyclotomic.Eval
/-!
# Primes congruent to one
We prove that, for any positive `k : ℕ`, there are infinitely ma... |
17,712 | lean_file_chunk | 9baf3ad27609cd228896322ae75636d18ca7b4554f29dd612514c073f579456a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen, Mantas Bakšys
-/
module
public import Mathlib.Data.Nat.Choose.Sum
public import Mathlib.NumberTheory.Padics.PadicVal.Basic
public import Mathlib.RingTheory.Ideal.Quotient.Defs
p... |
3,547 | lean_file_chunk | e5b373cc89138bbd711d11b42b3efa73c17dd3c59ccf05fef0ecc63ba1b72435 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Mathlib.Algebra.Field.ZMod
public import Mathlib.RingTheory.IntegralDomain
/-!
# The Lucas test for primes
This file implements the Lucas test f... |
374 | lean_file_chunk | 3f1bb8510040dc4a199f84311e718c35a4693f97f37bd89b55033fc6f9627097 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.NumberTheory.ArithmeticFunction.Defs
public import Mathlib.NumberTheory.ArithmeticFunction.Misc
public import Mathlib.NumberTheory.ArithmeticFunction.Moebius
public import Mathlib.NumberTheory.ArithmeticFunction.VonMangoldt
public import Mathlib.NumberTheory.ArithmeticFu... |
4,955 | lean_file_chunk | edde66eb65c5371720045e871ffe13de26612652a9c22a1bb689ceb802f62ced | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey, Ralf Stephan
-/
module
public import Mathlib.Data.Nat.Prime.Nth
public import Mathlib.Data.Nat.Totient
public import Mathlib.NumberTheory.SmoothNumbers
public import Mat... |
5,247 | lean_file_chunk | b27b07934dc7f4247bc9add70dd5b45b19a914f2ccdd957b7f51bd74eca9c029 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Yury Kudryashov, Bhavik Mehta
-/
module
public import Mathlib.Algebra.BigOperators.Associated
public import Mathlib.Algebra.Squarefree.Basic
public import Mathlib.Da... |
11,780 | lean_file_chunk | 432fc1f8bede7cbba1a7e580ebc75014889c506d9619d0a67cb480b78190210a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Paul Lezeau
-/
module
public import Mathlib.RingTheory.Conductor
public import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
public import Mathlib.RingTheory.IsAdjoinRoot
... |
15,348 | lean_file_chunk | a574954dc7d7fb60f65fa6e9212c75a200e615c7643ee79741b1fac01fce2bbd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.NumberTheory.LegendreSymbol.AddCharacter
public import Mathlib.NumberTheory.LegendreSymbol.ZModChar
public import Mathlib.Algebra.CharP.Ch... |
1,706 | lean_file_chunk | 79d279c168ddae415506a04f1081a11950afdde6bcc2638854d1b02173fbfdbe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Mathlib.FieldTheory.Finite.Basic
/-!
# Modular exponentiation with the totient function
This file contains lemmas about modular exponentiation.
... |
1,496 | lean_file_chunk | 3356e21f7f9d3599733729f3c0e771620bf3189f7641ce38d5bf2a8bc3e447a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
module
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.RingTheory.Ideal.Quotient.Defs
public import Mathlib.RingTheory.Ideal.Span
/-!
# ... |
23,980 | lean_file_chunk | e92d984cb552322264b85ef50a9c51f7befeb6e55a468316b89df8a55a37b25a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Algebra.IsPrimePow
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.Interval.Finset.Suc... |
6,205 | lean_file_chunk | 309207b64d09c46f583e792b870155be9911dab6447384f9bed3a97a5139a0a3 | lean_source_file | pkg_mathlib_source_file_chunks | theorem antidiagonal_map_subset_divisorsAntidiagonal_pow {q : ℕ} (hq : 1 < q) (k : ℕ) :
letI ι : ℕ ↪ ℕ := ⟨fun k ↦ q ^ k, Nat.pow_right_injective hq⟩
(Finset.antidiagonal k).map (.prodMap ι ι) ⊆ (q ^ k).divisorsAntidiagonal := by
intro k hk
obtain ⟨i, hi, rfl⟩ := Finset.mem_map.mp hk
simp [Nat.mem_divisor... |
8,922 | lean_file_chunk | e8a88296ebd1d0c0b8bb1415c78d0ad3b53f440986d88ec10b695bfb1f6f48b0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Colin Jones. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Colin Jones
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.NumberTheory.Divisors
public import Mathlib.Tactic.... |
9,189 | lean_file_chunk | 99377d9b0ee34527d006e19b6acfe12472287932f8ba3293ce7e3eabb7bc0593 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching, Ralf Stephan
-/
module
public import Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity
public import Mathlib.NumberTheory.LucasPrimality
/-!
# Fermat numbe... |
371 | lean_file_chunk | 33fcbe1af46e20f8a890f9dce117cab25f965e6a7b828e275f0f196b3453dc26 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Algebra.Order.Field.Power
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Data.EReal.Inv
public import Mathlib.NumberTheory.ArithmeticFunction.Misc
public import Mathlib.Topology.Algebra.InfiniteSum.Order
public import Mathlib.Topology.MetricSpace... |
9,433 | lean_file_chunk | 2b377d81f1346d9abe64ffe935f3ac5f64624115e98a67adc2aebf448c111010 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Arend Mellendijk. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arend Mellendijk
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.NumberTheory.ArithmeticFunction.Defs
/-!
# The Selberg Sieve
We set up the working assumptio... |
3,334 | lean_file_chunk | 7df574f64172a46ca2fb0f5e2d1fa778a6dfcdce0730126f9da378115632c575 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 John Nicol. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Nicol
-/
module
public import Mathlib.FieldTheory.Finite.Basic
/-!
# Wilson's theorem.
This file contains a proof of Wilson's theorem.
The heavy lifting is mostly done by the prev... |
17,012 | lean_file_chunk | 3db244c9e176641b7e052bedf5764be740f4105ac17af5adbd9c3bb80f21e886 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Niels Voss. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Niels Voss
-/
module
public import Mathlib.Algebra.Order.Archimedean.Basic
public import Mathlib.FieldTheory.Finite.Basic
public import Mathlib.Order.Filter.Cofinite
public import Mathlib... |
20,804 | lean_file_chunk | f559b28808ab190c0acc0d23b9ca20df26a4d14ea5d073b960f9098689699bf5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.Data.Nat.EvenOddRec
public import Mathlib.Tactic.Linarith
public import Mathlib.Tactic.LinearCombination
import Math... |
20,957 | lean_file_chunk | 8a6dc81de9682dc757ae1cad0204e7e1b5f6e5b3d778645d89f4ec9e24054cd0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.MeasureTheory.Function.Floor
public import Mathlib.MeasureTheory.Integral.Asymptotics
public import Mathlib.MeasureTheory.Integral.Integra... |
10,767 | lean_file_chunk | 29b7bc4e51154453dec6aca27e89fd2f95ed116672886dc7968df1ef8c7cf7d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alex Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Zhao, Daniel Buth, Sebastian Meier, Junyan Xu
-/
module
public import Mathlib.RingTheory.Ideal.NatInt
/-!
# Frobenius Number
In this file we first define a predicate for Frobenius n... |
10,650 | lean_file_chunk | aec0f5435754adc2d70880c897d797007072f28408ad59c5badf3e208dcf2d83 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero
-/
module
public import Mathlib.Algebra.Order.BigOperators.Ring.Multiset
public import Mathlib.Algebra.Polynomial.OfFn
public import Mathlib.Analysis.CStarAlgebra... |
23,974 | lean_file_chunk | 14e6159940939a8ac9e1d3a1caae657e5d156eff078bf85954d075114fb708c6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Alastair Irving, Kim Morrison, Ainsley Pahljina
-/
module
public import Mathlib.NumberTheory.Fermat
public import Mathlib.RingTheory.Fintype
/-!
# The Lucas-Lehmer test... |
2,067 | lean_file_chunk | ae52b3299267410e085f1e6eb4001ff5ff97a9df489f67cb422fcd5a6a243a17 | lean_source_file | pkg_mathlib_source_file_chunks | let .app _ (p : Q(ℕ)) ← Meta.whnfR e | failure
let ⟨ep, hp⟩ ← deriveNat p _
let np := ep.natLit!
unless 1 < np do
failure
haveI' h1ltp : Nat.blt 1 $ep =Q true := ⟨⟩
if sModNatTR (2 ^ np - 1) (np - 2) = 0 then
haveI' hs : sModNatTR (2 ^ $ep - 1) ($ep - 2) =Q 0 := ⟨⟩
have pf : Q(LucasLehmerTest $ep)... |
7,857 | lean_file_chunk | 1a220b8e0718e1471b3a9cc163f89c8f5ad4b223a49984e1849cf2d4ae8871fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Order.Ring.Rat
public import Mathlib.Data.Multiset.Sort
public import Mathlib.Data.PNat.Basic
public import Mathlib.Data.PNat.In... |
18,119 | lean_file_chunk | a56ce0900bf516e1e1de213ebafb8445c8615e0094ccb3d8071a2d0dec2888e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Dynamics.Ergodic.AddCircle
public import Mathlib.MeasureTheory.Covering.LiminfLimsup
/-!
# Well-approximable numbers and Gallagher's ergodic ... |
23,991 | lean_file_chunk | 980818bf7d089e0b3df8343abfee87718734c6f1b32594188dd17b8b9401e56b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Ralf Stephan
-/
module
public import Mathlib.Data.Nat.Factorization.Defs
public import Mathlib.Data.Nat.Squarefree
/-!
# Smooth numbers
For `s : Finset ℕ` we define th... |
1,332 | lean_file_chunk | e126db8e6364e07b29cabb5e469cc23b68118275037f444acf88d04f205a9329 | lean_source_file | pkg_mathlib_source_file_chunks | simp only [Finset.card_product, Finset.card_powerset, Finset.mem_range, zero_lt_succ,
Finset.card_erase_of_mem, Finset.card_range, succ_sub_succ_eq_sub, Nat.sub_zero]
/-- The set of `k`-rough numbers `≤ N` can be written as the union of the sets of multiples `≤ N`
of primes `k ≤ p ≤ N`. -/
lemma roughNumbersUpTo_e... |
9,991 | lean_file_chunk | 381465971483dbf58088e215ed2bc71a179275b39e79c38224e4449558902ca9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Ashvni Narayanan
-/
module
public import Mathlib.FieldTheory.RatFunc.Degree
public import Mathlib.RingTheory.DedekindDomain.IntegralClosure
public import Mathlib.RingTheory.... |
19,954 | lean_file_chunk | a9a75a1e57fc02d04eb3171f3c7e31894cda6aee0dade8e177e3c66d342e0955 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Alastair Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alastair Irving, Terry Tao, Ruben Van de Velde
-/
module
public import Mathlib.Algebra.Order.Floor.Semifield
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import Ma... |
23,965 | lean_file_chunk | 48fb5c4f8cb8c3cfde1f3fe6b9af9f5ff7a50fd08623b62633e90214caf51283 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Nat.ModEq
public import Mathlib.Data.Nat.Prime.Basic
public import Mathlib.NumberTheory.Zsqrtd.Basic
/-!
# Pell's equation and Mat... |
15,234 | lean_file_chunk | 81965dd523c02e9184ae448974e21449d8000b1585c43e33615b02f30cf766d5 | lean_source_file | pkg_mathlib_source_file_chunks | xn a1 i % xn a1 n < xn a1 j % xn a1 n
| 0, ij, _, _, _ => absurd ij (Nat.not_lt_zero _)
| j + 1, ij, j2n, jnn, ntriv =>
have lem2 : ∀ k > n, k ≤ 2 * n → (↑(xn a1 k % xn a1 n) : ℤ) =
xn a1 n - xn a1 (2 * n - k) := fun k kn k2n => by
let k2nl : 2 * n - k < n := by lia
have xle : xn a1 (2 * n -... |
21,015 | lean_file_chunk | 448892ba423cf8c79c86d6dac90eda58564a8df833d2fd8c33fe4154f6392c52 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata, Fabrizio Barroero, Laura Capuano, Nirvana Coppola,
María Inés de Frutos-Fernández, Sam van Gool, Silvain Rideau-Kikuchi, Amos Turchet,
Frances... |
23,989 | lean_file_chunk | e729dde81bf0e1c43dfbf6c72b25d60a8f88ba180bf130c460d77dd3831bfbaf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul van Wamelen
-/
module
public import Mathlib.Data.Int.NatPrime
public import Mathlib.Data.ZMod.Basic
public import Mathlib.RingTheory.Int.Basic
public import Mathlib.Tactic.Fiel... |
1,191 | lean_file_chunk | ab6e0be74e661f5d9b0dbb9fcc8e5c2192551027af9d3b58d6a7c2c0fcf6f1c7 | lean_source_file | pkg_mathlib_source_file_chunks | apply And.intro ht4
lia
· exfalso
revert h_pos
rw [h_neg]
exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (by positivity)))
exfalso
rcases h_even with ⟨rfl, -⟩
rw [mul_assoc, Int.mul_emod_right] at h_parity
exact zero_ne_one h_parity
/-- **Formula for Pythagorean... |
2,286 | lean_file_chunk | 15f7baff1e5df99b87f7b06fec1f0feba9265f4acdff74dfb56580cd5b1e075f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
module
public import Mathlib.FieldTheory.KrullTopology
public import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
public import M... |
2,463 | lean_file_chunk | 8c4d3a1c3f119165cd4225349f876bb79b799848a3760e631ea2a7f81dd1eb0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot, Kenny Lau
-/
module
public import Mathlib.Algebra.Algebra.Rat
public import Mathlib.Algebra.Field.ZMod
public import Mathlib.Algebra.CharP.Algebra
public import Mathlib.... |
15,485 | lean_file_chunk | 69e99a556bb22e71ee98de466b42a8ae881a1c490c532ceefcb4cf39cfb23d80 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
module
public import Mathlib.FieldTheory.AlgebraicClosure
public import Mathlib.FieldTheory.PolynomialGaloisGroup
public import Math... |
11,502 | lean_file_chunk | 1759decf36a03ca660f61eb7fe8d7f17a73a9f5b670c533c653e435c84e25380 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.RingTheory.Algebraic.Basic
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.ModelTheory.Algebra.Field.IsAlgClosed
public ... |
16,551 | lean_file_chunk | 27ad4b34c34579e455cbc5210db341c541f424b198f4643a986539e4a67868af | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Christian Merten, Junyan Xu
-/
module
public import Mathlib.Algebra.CharP.IntermediateField
public import Mathlib.Algebra.MvPolynomial.Nilpotent
public import Mathlib.Algebr... |
9,689 | lean_file_chunk | 0b46208b59ffe897557c6d0d5057e1416e759d9e953caf80a1df1b495e1715f0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 F. Nuccio, H. Zheng, W. He, S. Wu, Y. Yuan, W. Jiao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Huanyu Zheng, Sihan Wu, Wanyi He, Weichen Jiao, Yi Yuan
-/
module
public import Mathlib.Algebra.Central.Defs
public import M... |
3,696 | lean_file_chunk | 4b354691a0f571f66af2b0f2e10ccaf899fd6c6819a176f15a93e9b842a340e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.Polynomial.Taylor
public import Mathlib.FieldTheory.RatFunc.AsPolynomial
/-!
# Laurent expansions of rational functions
## M... |
23,986 | lean_file_chunk | b0232cbc175278ee074b33387d41f2fd5d7458f0f056feae4fd76930bc46a4d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.FieldTheory.SplittingField.Construction
public import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
public import Mathlib.FieldTheory.Separable
publi... |
21,828 | lean_file_chunk | 58b763ad49e8475901970bb64765ae6bb4c68c6a5898506d4284b4a71149a14e | lean_source_file | pkg_mathlib_source_file_chunks | end Polynomial
namespace Irreducible
variable {F}
variable {f : F[X]}
/-- The separable degree of an irreducible polynomial divides its degree. -/
theorem natSepDegree_dvd_natDegree (h : Irreducible f) :
f.natSepDegree ∣ f.natDegree := by
obtain ⟨q, _⟩ := ExpChar.exists F
have hf := h.hasSeparableContraction... |
20,403 | lean_file_chunk | 041b5e876d9f5c8ef837dc8e139e9718f8c78a6cd2e000693170bd661b3fd049 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.CharP.Basic
public import Mathlib.Algebra.CharP.Reduced
public import Mathlib.FieldTheory.KummerPolynomial
public import Mathlib.Field... |
22,811 | lean_file_chunk | fbd1af3d2d5570fa0f3bef63d0e93d00ff39cd19874e2a2e95ac89cb8f52db97 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.FieldTheory.PurelyInseparable.Basic
public import Mathlib.FieldTheory.PerfectClosure
/-!
# `IsPerfectClosure` predicate
This file contains `IsPerfect... |
16,267 | lean_file_chunk | 9b72d63850eb88c654ee0347bb91a97ee951991e756cfb32d15cda84a16d1e6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
module
public import Mathlib.FieldTheory.Galois.Basic
/-!
# Galois Groups of Polynomials
In this file, we introduce the Galois group ... |
5,631 | lean_file_chunk | a8b5eaf92dc709454ea0d7870784efc757a95e8eca7776bff3e41ea4e6547431 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Andrew Yang, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.AdjoinRoot
public import Mathlib.RingTheory.Norm.Defs
/-!
# Irreducibility of X ^ p - a
## Main result
- `X_pow_sub_... |
1,861 | lean_file_chunk | ba5e417cfb15d65b00c1e62a5d88f8985f3b3170c6c560423b5eae809d0b24f7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.RingTheory.Noetherian.Basic
/-!
# Finiteness of `IsScalarTower`
We prove that given `IsScalarTower F K A`, if `A` is finite as a module over `F`... |
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