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 |
|---|---|---|---|---|---|
23,939 | lean_file_chunk | 51e1d42acbe495198303d1bd4f2f82525b93130cdb1e27c8b6df4d25a732a830 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Copy
public import Mathlib.Combinatorics.SimpleGraph.Operations
public import Mathlib.... |
14,242 | lean_file_chunk | e5656a3964c7e2ead6ec5c0d3a8956367e18426a7ab284e18969108f54f4e6f3 | lean_source_file | pkg_mathlib_source_file_chunks | theorem mem_cliqueSet_iff : s ∈ G.cliqueSet n ↔ G.IsNClique n s :=
Iff.rfl
@[simp]
theorem cliqueSet_eq_empty_iff : G.cliqueSet n = ∅ ↔ G.CliqueFree n := by
simp_rw [CliqueFree, Set.eq_empty_iff_forall_notMem, mem_cliqueSet_iff]
protected alias ⟨_, CliqueFree.cliqueSet⟩ := cliqueSet_eq_empty_iff
@[gcongr, mono]
... |
7,940 | lean_file_chunk | 49e960924ab72bb237bfae376e06bf6d2edf861ee2027ac171fd942933af438c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Iván Renison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Iván Renison
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Bipartite
public import Mathlib.Combinatorics.SimpleGraph.Circulant
public import Mathlib.Combinatorics.SimpleGrap... |
7,749 | lean_file_chunk | e5d7a2270f1c5064192a77ca6400b3bfc2ff8fed3beb775ec597547f989d520d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Ella Yu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Ella Yu
-/
module
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public import Mathlib.Data.Finset.Prod
public import Mathlib.Data.Fintype.Prod
publ... |
2,611 | lean_file_chunk | a397b4da02e03c58d5e854323ebc30c7ed6714f297d5bd73b5c203a0a950c00c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Finset
public import Mathlib.Data.Real.Basic
public import Mathlib.Order.Preorder.Finite
public import Mathli... |
8,149 | lean_file_chunk | c370720182e8df8bad755c5948368d87890b0466f9db71b4e4d5bde4be2fc1f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Additive.PluenneckeRuzsa
public import Mathlib.Data.Fin.VecNotation
public import Mathlib.Data.Real.Basic
public import Mathli... |
4,857 | lean_file_chunk | 3cb7a0c177084ba2a0d59281f6f0a01ad032615784572e14768f0ad595b79fab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Strahinja Gvozdić, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Strahinja Gvozdić, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Finset
/-!
# Convolution
This file define... |
6,356 | lean_file_chunk | 9e5508a54bfd658209f0e0d16a85f940b573d0d36d14a51467f9639d5fb41fc2 | 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.Algebra.Group.Action.Pointwise.Finset
public import Mathlib.Algebra.Ring.Nat
/-!
# e-transforms
e-transforms are a family of transformatio... |
6,984 | lean_file_chunk | cf7d44f5168295d58b72c10724aa272366e22cf33d69dc0b7167877b56442b79 | 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.Algebra.BigOperators.Group.Finset.Piecewise
public import Mathlib.Algebra.Group.Pointwise.Set.Basic
public import Mathlib.Algebra.Group.Unit... |
23,965 | lean_file_chunk | b9049571e24ba70fe831d9fec5a38916d7ebfe2baef1d599622befc05a0f0a7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies, Patrick Luo, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Patrick Luo, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Pointwise.Stabilizer
public import Mathlib.Combinatorics.Additive.Convolution
... |
16,477 | lean_file_chunk | be6247a3074ba6d7f0b0fdcf1afc69ae3bcd415b8ed217ed376033b6a958dc5b | lean_source_file | pkg_mathlib_source_file_chunks | have : (0 : ℝ) < #((z⁻¹ •> A) ∩ (w •> A)) := by
have : (#((A ∩ z⁻¹ •> A) ∩ (A ∩ w •> A)) : ℝ) ≤ #(z⁻¹ •> A ∩ w •> A) := by
gcongr <;> exact inter_subset_right
have : (#((A ∩ z⁻¹ •> A) ∪ (A ∩ w •> A)) : ℝ) ≤ #A := by
gcongr; exact union_subset inter_subset_left inter_subset_left
have :
... |
9,030 | lean_file_chunk | 4c0ee1774a65f8369cf7c45fdfbdbe405919cf3f325940cfb73ec7a877cddd22 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Group.Subgroup.Pointwise
public import Mathlib.Combinatorics.Additive.CovBySMul
public import Mathlib.Combinatorics.Ad... |
9,282 | lean_file_chunk | 94d12b2e11aea212370308cdf479aeb53536c134a2f7ecaeea57caf9810fe477 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Additive.PluenneckeRuzsa
public import Mathlib.Data.Finset.Density
/-!
# Doubling and difference constants
This file defines... |
2,783 | lean_file_chunk | 0d81f1aaa4306af69aef49b5f5f8e6f7c505369086689821c56c75eac1bc53dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.Group.Pointwise.Finset.Scalar
public import Mathlib.Data.Real.Basic
p... |
5,119 | lean_file_chunk | 4b827db6f342c3856d12f54358adea195ec6f7b6069cb8c79288a9a47bbba0e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Aviv Bar Natan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aviv Bar Natan
-/
module
public import Mathlib.Algebra.Group.Action.Defs
public import Mathlib.Algebra.Group.Pointwise.Finset.Scalar
public import Mathlib.Algebra.Order.Monoid.Defs
pu... |
2,361 | lean_file_chunk | 0d9a92d835c6236af0a35042d03c1f7d74fffe1e5c45d196d5ead10c1be53bec | 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.Analysis.Fourier.FiniteAbelian.Orthogonality
public import Mathlib.Combinatorics.Additive.Dissociation
/-!
# Randomising by a function of d... |
13,267 | lean_file_chunk | 1a949d8445ecec1a10b495c3e31a2bcc9ba80aae67916b07c2c819dba90e6655 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, George Shakan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, George Shakan
-/
module
public import Mathlib.Algebra.Order.Field.Rat
public import Mathlib.Combinatorics.Enumerative.DoubleCounting
public import Mathlib.T... |
10,245 | lean_file_chunk | 56ab62996d07689924706d5a2f855754182d5f7f11e0c85faab014838c006cd6 | 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.Algebra.BigOperators.Ring.Finset
public import Mathlib.Data.Multiset.Fintype
public import Mathlib.FieldTheory.ChevalleyWarning
/-!
# The E... |
11,464 | lean_file_chunk | e4edc8cef0d209d66fdb576538ae9e5886c18e8504f11c7d366186e94ef066ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.Additive.ETransform
public import Mathlib.GroupTheory.Order.Min
/-!
# The Cauchy-Davenport theore... |
19,249 | lean_file_chunk | 23e2ddb85c09c324b299835c7f625f6c2da2eebdf0efe5a9fe706f87b9a6cf1f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.CharP.Basic
public import Mathlib.Algebra.Group.Pointwise.Set.B... |
10,970 | lean_file_chunk | 4cc157874c8399defac821aba03455395b99eedeb0a4740fc350311d49749f1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Finite
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.Group... |
5,160 | lean_file_chunk | ba05d5d68a10a7df510ffe78d11a036e0c7b50166f91a3d04b20a8744b4a302a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jake Levinson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jake Levinson
-/
module
public import Mathlib.Combinatorics.Young.YoungDiagram
/-!
# Semistandard Young tableaux
A semistandard Young tableau is a filling of a Young diagram by natur... |
15,616 | lean_file_chunk | 31d92e9370ea2ec8d923781a67a4af489a7666d112a835f65bccdd59ecf754ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jake Levinson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jake Levinson
-/
module
public import Mathlib.Data.Finset.Preimage
public import Mathlib.Data.Finset.Prod
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Order.UpperLowe... |
10,308 | lean_file_chunk | c9d31fe7a9d1b7ee8490af86af4c14273892f57b95e138315de779514ff10351 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Bhavik Mehta, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
module
public import Mathlib.Algebra.Field.Basic
public import Mathlib.Algebra.Field.Rat
public import Mathlib.Combinatorics.E... |
12,340 | lean_file_chunk | 9b9a1491ebecf02ede78afc3107b0f0e1bb09241253cae924cd95225b8e0b9a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
module
public import Mathlib.Data.Finset.Grade
public import Mathlib.Data.Finset.Sups
public import Mathlib.Logic.Function.Iterate
/-!
# Sh... |
9,078 | lean_file_chunk | c94ec1f54f3327b05ba30bc20b331cfcf6fcd38c41ce220c171d8ed8df16ca48 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Order.UpperLower.Basic
/-!
# Intersecting families
This file defines intersecting families and pro... |
19,406 | lean_file_chunk | 78c4d1a2fad86cc31f780af0792ce6e9719b8ce010d50f653ecaa4d640d81ce3 | 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.Algebra.BigOperators.Group.Finset.Piecewise
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Orde... |
18,538 | lean_file_chunk | e74cbdec7c7f9b39563ce0e32a342c21e644e7837dce55cb43e4822df82e16d9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
module
public import Mathlib.Combinatorics.Colex
public import Mathlib.Combinatorics.SetFamily.Compression.UV
public import Mathlib.Combinatorics.SetFamily... |
19,432 | lean_file_chunk | a113581bbdb5c5931e7a0966c5fa4d89f59be99297fbcb5b195c038ea6240b35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Vladimir Ivanov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Vladimir Ivanov
-/
module
public import Mathlib.Algebra.BigOperators.Intervals
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathli... |
3,812 | lean_file_chunk | ea17d337698d29a5eebed9b9dedb4ef3e4d6e044db8479af68f7928e7ed0800f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.HarrisKleitman
public import Mathlib.Combinatorics.SetFamily.Intersecting
/-!
# Kleitman's bound on the size of int... |
5,570 | lean_file_chunk | dd9ab57b8659ccc5d9f64c3f2135fe6c86632ede0f76c625d2a316dc81f0c17f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Ring.Canonical
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Combinatorics.SetFamily.Compression.Down
pub... |
8,358 | lean_file_chunk | ec5cd702ed589440216b4d541b09c8b290dd3a41220e15b1dd9bc438b6f1c73b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Compression.Down
public import Mathlib.Data.Fintype.Powerset
public import Mathlib.Order.Interval.Finset.Nat
public ... |
9,862 | lean_file_chunk | f042354e25a6547919b6ed2c9776fdf496a80bdb445f5ea7f528558b1450cfd2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller
-/
module
public import Mathlib.Data.Fintype.Basic
public import Mathlib.Data.Fintype.Powerset
public import Mathlib... |
9,282 | lean_file_chunk | 7fcc8baae1c52c0276eee8b99c9f94cf200c25a45be9cc29c647b58e15c09dd3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller
-/
module
public import Mathlib.Combinatorics.Hall.Finite
public import Mathlib.CategoryTheory.CofilteredSystem
publ... |
11,483 | lean_file_chunk | d67b55013f4f43bc3ef2e0706040931894b49deb2c9f0c98c10742461cad9395 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Additive.AP.Three.Behrend
public import Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite
public import Mathlib.Tactic.Rif... |
4,647 | lean_file_chunk | 4268472bb3b5a942a7c048fc205a98e99261d68a26e476e677ca4b7b31450b19 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Combinatorics.Derangements.Basic
public import Mathlib.Data.Fintype.BigOperators
pu... |
1,965 | lean_file_chunk | 224bb3da57172c30b3d7ac7d780226b4b4d895f1aa9491b52e4f47f9798f441c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson, Patrick Massot
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Analysis.SpecialFunctions.Exponential
public import Mathlib.Combinatorics... |
8,275 | lean_file_chunk | 56d18fa733a1cc2bfdaa6f065710f2ee26d4fb57f42e420c85251395098eb6bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
module
public import Mathlib.Dynamics.FixedPoints.Basic
public import Mathlib.GroupTheory.Perm.Option
public import Mathlib.Logic.Equiv.Defs
public import Mathlib.Logi... |
2,854 | lean_file_chunk | 1f9afc203fbdcaef80b44beceeed605f3bf3be8fddadd13ac147ab20efe8fa7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rida Hamadani. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rida Hamadani
-/
module
public import Mathlib.Combinatorics.Digraph.Basic
public import Mathlib.Combinatorics.SimpleGraph.Basic
/-!
# Graph Orientation
This module introduces conver... |
8,035 | lean_file_chunk | 7e53591a7d1dedaeb67acf61685bea78457d300382ebf6f3103df82712450245 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kyle Miller, Jack Cheverton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Jack Cheverton, Jeremy Tan
-/
module
public import Mathlib.Order.CompleteBooleanAlgebra
public import Mathlib.Data.Fintype.Pi
/-!
# Digraphs
This module de... |
8,594 | lean_file_chunk | f1a0d896317dfdc11c215435e9ed114f7fef26d38f0be78d32866e6f6bbc6367 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Algebra.Order.Antidiag.Finsupp
public import Mathlib.Combinatorics.Enumerative.Composition
public import Mathlib.Tactic.ApplyFun
/-!
# Part... |
9,369 | lean_file_chunk | 05f38f142ddeec3ec9ab096608e5308829f1014145fa75534427d4fdf29c6200 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
module
public import Mathlib.Combinatorics.Enumerative.Partition.Basic
public import Mathlib.RingTheory.PowerSeries.PiTopology
/-!
# Generating functions for partitions
Th... |
6,364 | lean_file_chunk | 7fc78e30bbc1d4ac7e5b36395e777d63c8afe7efea7f4a2c9d7651298a9cfe32 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
module
public import Mathlib.Combinatorics.Enumerative.Partition.GenFun
public import Mathlib.RingTheory.PowerSeries.NoZeroDivisors
/-!
# Glaisher's theorem
This file prov... |
2,228 | lean_file_chunk | a99658193f6fcf20b2a074beaaccbad4f4f9688aee5041eeb102391f1ad2f7c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Matteo Cipollina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Combinatorics.Quiver.Path
/-!
# Path Decomposition and Boundary Crossing
This sectio... |
9,030 | lean_file_chunk | d82d9ae3ce0ace2516c6e6dab373810e9aba4c5513499b1921e54e27ef336c2d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Matteo Cipollina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Combinatorics.Quiver.Path
public import Mathlib.Data.Set.Insert
public import Mathlib.... |
4,697 | lean_file_chunk | b1249a99737863e42284606eeef2ab866288aa1e27e6729054506092bb816f82 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Matteo Cipollina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina
-/
module
public import Mathlib.Combinatorics.Quiver.Path
public import Mathlib.Algebra.Order.Ring.Defs
/-!
# Path weights in a Quiver
This file defines the weig... |
8,130 | lean_file_chunk | 196d2a3d64aeb8129c8d30bb42acf293bcf932e8c15ae0da2491c423c8c72396 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Combinatorics.Matroid.Closure
/-!
# Finite-rank sets
`Matroid.IsRkFinite M X` means that every basis of the set `X` in the matroid `M` is... |
23,967 | lean_file_chunk | 3cd89f56ebb5974f082768dc3ef655034c1d840fa33b28e86e9bbfc4fa5dfaf4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Combinatorics.Matroid.Rank.Finite
public import Mathlib.Combinatorics.Matroid.Loop
public import Mathlib.Data.ENat.Lattice
public import Mat... |
5,074 | lean_file_chunk | 45cca473d49bef5af4282ccb7fc97cf268296205418f9e9af7f1bfae187064ec | lean_source_file | pkg_mathlib_source_file_chunks | lemma eRk_le_one_iff [M.Nonempty] (hX : X ⊆ M.E := by aesop_mat) :
M.eRk X ≤ 1 ↔ ∃ e ∈ M.E, X ⊆ M.closure {e} := by
refine ⟨fun h ↦ ?_, fun ⟨e, _, he⟩ ↦ ?_⟩
· obtain ⟨I, hI⟩ := M.exists_isBasis X
rw [hI.eRk_eq_encard, encard_le_one_iff_eq] at h
obtain (rfl | ⟨e, rfl⟩) := h
· obtain ⟨e, he⟩ := M.grou... |
19,504 | lean_file_chunk | 7967c9348ba687962e9247fa51a0761dc1e3b277c3088b865d32d53eb93020e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson and Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson, Junyan Xu
-/
module
public import Mathlib.Combinatorics.Matroid.Map
public import Mathlib.Combinatorics.Matroid.Rank.ENat
public import Mathlib.Combinatorics... |
5,601 | lean_file_chunk | 4f13b26ce4b6435d00d6808f6edaeed1ad3259c1e5d8ba92eab83bd249dccb53 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Combinatorics.Matroid.Minor.Contract
/-!
# Matroid Minors
A matroid `N = M ／ C ＼ D` obtained from a matroid `M` by a contraction then a de... |
21,107 | lean_file_chunk | 6e94d9dc1c8f689f9b2d94d7ba220c3b681cab05865e328e06c9ffd6be1e9040 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Combinatorics.Matroid.Dual
/-!
# Matroid Restriction
Given `M : Matroid α` and `R : Set α`, the independent sets of `M` that are contained... |
23,981 | lean_file_chunk | f83c716f422b4319f59e45e7af97329c17952b2de3bdefcd2e3a77d22b294471 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Combinatorics.Matroid.Minor.Delete
public import Mathlib.Tactic.TautoSet
/-!
# Matroid Contraction
Instead of deleting the elements of `X ... |
4,036 | lean_file_chunk | 7e29aee088bfa5c6833ed2fc2349c860dca0531a455b4460661959c980cb6232 | lean_source_file | pkg_mathlib_source_file_chunks | lemma IsCocircuit.delete_diff_isCocircuit {X : Set α} (hK : M.IsCocircuit K) (hXK : X ⊆ K)
(hX : X.Nonempty) : (M ＼ (K \ X)).IsCocircuit X := by
rw [isCocircuit_def, dual_delete]
exact hK.isCircuit.contract_diff_isCircuit hX hXK
/-! ### Commutativity -/
lemma contract_delete_diff (M : Matroid α) (C D : Set α)... |
9,990 | lean_file_chunk | c20879d40b95103555c13a4fe4e0d8960dc10f5fbbedc8c177dad665e19885fa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Combinatorics.Matroid.Loop
/-!
# Matroid Deletion
For `M : Matroid α` and `X : Set α`, the *deletion* of `X` from `M` is the matroid `M ＼ ... |
8,759 | lean_file_chunk | eefe317815396971aec04602bf8cde84d309bd2efcd66bd51bc687bdc56623c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Rémi Bottinelli, Yaël Dillies
-/
module
public import Mathlib.Combinatorics.SimpleGraph.DeleteEdges
public import Mathlib.Combinatorics.SimpleGraph.Walk.Operations
/-!
# Ma... |
13,160 | lean_file_chunk | a5f62e67e7ba37cbb3ee03ca80e8b6a8e9c5641f6d51f8a10ce70f6afeac5933 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Pim Otte
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Walk.Operations
public import Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks
/-!
# Decomposing walks
## ... |
11,168 | lean_file_chunk | 57c777dd91fb099dd9981b3ea48b0689a7d28ffc3118b4167a1bafa100e542a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Daniel Weber
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Walk.Basic
/-!
# Traversing walks
Functions that help access different parts of a walk.
## Main def... |
18,039 | lean_file_chunk | f7ed4e9731975a221072c3b3241718b30d3ca9ab480c597031f9fb536143fa42 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Peter Nelson
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Dart
/-!
# Walks
In a simple graph, a *walk* is a finite sequence of adjacent vertices, and can be
t... |
7,079 | lean_file_chunk | b17e3581ab1b6be6b9f11450495a4f73d148ccc49c793ac4845fbc7b576a02ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Paths
/-!
# Counting walks of a given length
## Main definitions
- `walkLengthTwoEquivCommonNeighbors`: bijective ... |
23,968 | lean_file_chunk | 865c0534dcf0bb6db8e80d0f43c16171134781011dbc2c6446b64a861be99e78 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Pim Otte, Daniel Weber, Rida Hamadani
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Walk.Traversal
public import Mathlib.Data.List.Zip
/-!
# Operations on walks... |
6,491 | lean_file_chunk | 6b2f0ce25c5d63f4d610a56e9d23eed9a1864a07b8fa4247f76c21ee23daa5da | lean_source_file | pkg_mathlib_source_file_chunks | lemma penultimate_concat {t u v} (p : G.Walk u v) (h : G.Adj v t) :
(p.concat h).penultimate = v := by simp [concat_eq_append, getVert_append]
@[simp]
lemma snd_reverse (p : G.Walk u v) : p.reverse.snd = p.penultimate := by
simpa using getVert_reverse p 1
@[simp]
lemma penultimate_reverse (p : G.Walk u v) : p.r... |
9,550 | lean_file_chunk | c0655641f1d07d989e4f0c17e140ebcd2d1031ce15471a7a56a4ff3b49aec7bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rida Hamadani. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rida Hamadani
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Walk.Maps
public import Mathlib.Combinatorics.SimpleGraph.Walk.Operations
public import Mathlib.Combinatorics.Si... |
5,444 | lean_file_chunk | 68dc619eb0720ad8a9b607b15c72361d9ab6834d489d495746e5d1421f0564ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Nat
public import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
public import Mathlib.Combinatorics.Simpl... |
8,534 | lean_file_chunk | a9ecb4631be1bc8d497729bfee363b35abf7af53be91061976309efb3d267f67 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Youheng Luo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Youheng Luo
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
public import Mathlib.Data.Set.Card
/-!
# Edge Connectivity
This file defines k-edge-connec... |
3,229 | lean_file_chunk | 627a3171ccacad3d5cc0cbf0941478333a6810c56eaa55229b6b1d49122bd456 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Otte
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite
public import Mathlib.Data.Set.Card
/-!
# Representation of components by a set of vertices
## Main ... |
23,991 | lean_file_chunk | e166f498b99e6c443047ae59898a09c7af45051aa32d8fbc0bacc8745ab58c35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Paths
public import Mathlib.Combinatorics.SimpleGraph.Subgraph
public import Mathlib.Combinatorics.SimpleGraph.Opera... |
16,123 | lean_file_chunk | b57f5da7dd8895157ba6c298ee433c0d491517a02d478fabf2a881fd858ca0d6 | lean_source_file | pkg_mathlib_source_file_chunks | refine ⟨fun ⟨_, ⟨hi, hi'⟩⟩ ↦ hi hi', ?_⟩
intro hv
use G.connectedComponentMk v
use c'.connectedComponentMk_supp_subset_supp h hv
simp only [mem_supp_iff]
lemma top_supp_eq_univ (c : ConnectedComponent (⊤ : SimpleGraph V)) :
c.supp = (Set.univ : Set V) := by
obtain ⟨w, rfl⟩ := c.exists_rep
ext v
simpa... |
23,987 | lean_file_chunk | dc13f9214c87bec82a5b597e6d19f442afd8cbb243865cf4472672bd329f195e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Rémi Bottinelli
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
public import Mathlib.Data.Set.Card
/-!
# Connectivity of ... |
7,459 | lean_file_chunk | 9791ac3a01e36b3759f13960c709ed27d8cc76b330e5163f59a8f50873160640 | lean_source_file | pkg_mathlib_source_file_chunks | rw [Subgraph.preconnected_iff]
rintro ⟨u, hu⟩ ⟨v, hv⟩
obtain ⟨p, h⟩ := hw hu hv
exact Reachable.map (Subgraph.inclusion h)
(p.toSubgraph_connected ⟨_, p.start_mem_verts_toSubgraph⟩ ⟨_, p.end_mem_verts_toSubgraph⟩)
lemma connected_iff_forall_exists_walk_subgraph (H : G.Subgraph) :
H.Connected ↔
... |
11,633 | lean_file_chunk | 9b19cbdd9bb5cc006050285cd5f36c51960e6e89bd1a945b2a4969657a3bacf3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Triangle.Basic
/-!
# Construct a tripartite graph from its triangles
This file conta... |
12,391 | lean_file_chunk | 6323f67704cd6d01a5b7eba1e7146a61dc17a85e4163595d71e6c0f8400e37cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.Combinatorics.Enume... |
7,679 | lean_file_chunk | ade3aecb244ca87f99a2c71e14dd881287d6c38638d21bcf89d1c2ac6e5e1ede | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Clique
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform
public impor... |
8,818 | lean_file_chunk | e5b7d3502c21e91387442e59e5ae2172479cfe6442cba7318a9bd575736f2370 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.DegreeSum
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma
public impo... |
2,105 | lean_file_chunk | 15168529f54a04986237d5c004e6bbc16f339b4938d47be0da8e3fa8f08c0693 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Module.NatInt
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Combin... |
18,911 | lean_file_chunk | ef21f70c5f9b2b33d657b6ff50521bfc88c1e59ebc5bf89cc487c2241f8e7b40 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Combinatorics.SimpleGraph.Density
public import Mathlib.D... |
10,479 | lean_file_chunk | ef14509fc16c37a4b476f59f49105b5cd8b1d5af80cf544c60893076a7efd1aa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Order.Ring.Canonical
public import Mathlib.Order.Partition.Equipartition
/-!
# Equitabilising a partiti... |
10,602 | lean_file_chunk | cf72621b9f208bd332c3fcb4ffcd856e1f8fe211535fa365a28e0437dd36c411 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Algebra.Order.Chebyshev
public import Mathlib.Analysis.SpecialF... |
23,942 | lean_file_chunk | 1289a03265fe3bb4ed6ac7d9478519b3f6164628728a6752c2eff36cb027a134 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Bound
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabili... |
1,880 | lean_file_chunk | bd3319c749af1252fc63f8ce0187e0a06a335edf2de9e30286bf4290b5142c97 | lean_source_file | pkg_mathlib_source_file_chunks | have t : (star hP G ε hU V).product (star hP G ε hV U) ⊆
(chunk hP G ε hU).parts.product (chunk hP G ε hV).parts :=
product_subset_product star_subset_chunk star_subset_chunk
have hε : 0 ≤ ε := by sz_positivity
have sp : ∀ (a b : Finset (Finset α)), a.product b = a ×ˢ b := fun a b => rfl
... |
7,863 | lean_file_chunk | 4a1481e6d8e02a7b04049659161ad059d9076dd33e21a8e2fb92e9b5e8934708 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Increment
/-!
# Szemerédi's Regularity Lemma
In this file, we prove Szeme... |
8,416 | lean_file_chunk | c3edc4fdf5b9034c828c404763dcc52c1b513621be3266b7e3470cce5bdd758f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk
public import Mathlib.Combinatorics.SimpleGraph.Regularity.Energy
/-... |
23,965 | lean_file_chunk | 3645b1e1e7481ced339909fd8ee93d9a0eaaa3a98f820d8f6f71e492427cc0c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Kyle Miller
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Clique
public import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
public import Mathl... |
664 | lean_file_chunk | da7a9bd94f0e2f43c5678ec5c87355258a93c4c4510271f992f4c1a47b163fe2 | lean_source_file | pkg_mathlib_source_file_chunks | (completeMultipartiteGraph V).Colorable (n - 1) := by
cases n with
| zero => exact absurd hc not_cliqueFree_zero
| succ n =>
have : Fintype ι := fintypeOfNotInfinite
fun hinf ↦ not_cliqueFree_of_infinite V f hc
apply (coloring V).colorable.mono
have := not_cliqueFree_of_le_card V f le_rfl
contrapose! ... |
11,225 | lean_file_chunk | 34471b9a3486be651711d781a4af22f55dab819de79781ca01f92a20cde613e4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anand Rao, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anand Rao, Rémi Bottinelli
-/
module
public import Mathlib.CategoryTheory.CofilteredSystem
public import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
public im... |
1,862 | lean_file_chunk | 6d0e5fd3adf7f7c2505fc683a8874b8cbc196b297a6e94da3072a9e36aa25dd4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anand Rao, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anand Rao, Rémi Bottinelli
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Ends.Defs
public import Mathlib.CategoryTheory.CofilteredSystem
/-!
# Properties of t... |
8,121 | lean_file_chunk | 6f012b4204b46530a613a63a4b56c7750211aa85f8e859656a68c4329d6c67eb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Mitchell Horner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Horner
-/
module
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Combinatorics.SimpleGraph.Copy
/-!
# Extremal graph theory
This file introduces b... |
19,874 | lean_file_chunk | ac35c0ba5f02cb3d8baebae8ba986345cb8d961f9f8ce387883f37e1e0e6ecda | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Clique
public import Mathlib.Combinatorics.SimpleGraph.Extremal.Basic
public import Mathlib.Combinatorics.SimpleGraph.... |
7,446 | lean_file_chunk | 12c83c8f182012fba5eda947274ab496578dff53b5e9cce9186b41988ad5ebaa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Mitchell Horner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Horner
-/
module
public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
public import Mathlib.Combinatorics.Enumerative.DoubleCounting
public import Mathlib.Combina... |
2,626 | lean_file_chunk | 846d0bef334d428f9fb624d41a90721237ced5f93c5b5c39effcf48d3da8a585 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Combinatorics.SimpleGraph.Copy
public import Mathlib.Topology.MetricSpace.Defs
/-!
# Unit-distance graph embeddings
An embedding of a graph in... |
4,636 | lean_file_chunk | 96ddf4b884800bf9ed995fde34556381004ba0f470e74f25e4529892292e5443 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Additive.FreimanHom
/-!
# Corners
This file defines corners, namely triples of the form `(x, y), (x, y + d), (x + d, y)`, an... |
8,681 | lean_file_chunk | 18dda32b36c66f61ae630c2ea835befe85a0140d6fab404bf990a9dcaca1c17d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.Additive.AP.Three.Defs
public import Mathlib.Combinatorics.Additive.Corner.Defs
public import Math... |
20,504 | lean_file_chunk | 7397970bdd1d449483a4b019c48e49cd1f3a729db6bda43e93a3b7fba8f7d15c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Analysis.Complex.ExponentialBounds
public import Mathlib.Analysis.InnerProductSpace.Convex
public import Mathlib... |
18,755 | lean_file_chunk | 156f5d8267288fd0fd91d48d179fd9c40f954ea4426f92ca05766a4d13604ee2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Defs
public import Mathlib.Algebra.Order.Interval.Finset.Basic
public import Mathli... |
16,848 | lean_file_chunk | ee51a3e166485c8effd0863efa9ec62288f5e9d6a1b5e740a22fbed9bfa285b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Combinatorics.SetFamily.Shadow
/-!
# UV-compressions
This file defines UV-compression. It is an operation on a set family th... |
10,954 | lean_file_chunk | 674b972d0f56b65df3f1ec07afa7821134367d3f0d0523e64cd196b14a90a55a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Finset.Card
public import Mathlib.Data.Finset.Lattice.Fold
/-!
# Down-compressions
This file defines down-compression.
Down-compress... |
7,347 | lean_file_chunk | b01e6cad9609d35b501af3280ca63cc6b97fe343b8badd4eebc99de00ed7b2db | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.BilinearForm.Hom
public import Mathlib.LinearAlgebra.Dual.Lemmas
public import Mathlib.LinearAlgebra.TensorProduct.Tower
public ... |
5,602 | lean_file_chunk | dfcc307b4b0fe0d4a7a781b82935340d4d574b949ff63808811b3e9dca8b77cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.BilinearForm.Properties
/-!
# Dual submodule with respect to a bilinear form.
## Main definitions and results
- `BilinForm.du... |
4,720 | lean_file_chunk | 78a2d78baeac118d713cc64569056a048eac2bcdc1c7b36fe469ee6599873da1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
module
public import Mathlib.Algebra.Algebra.Tower
public import Mathlib.LinearAlgebra.BilinearMap
/-!
# Bilinear form
This file defines a bilinea... |
15,597 | lean_file_chunk | ddfa644d70201ed7aafd01226d540a061db9a3c63ca49b38df6f395ece120e39 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
module
public import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
public import Mathlib.LinearAlgebra.BilinearForm.Properties
/-!
# Bilinear form
... |
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