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 |
|---|---|---|---|---|---|
17,858 | lean_file_chunk | 691bd3d6219ce86dc641cae31da2a814615a6249555af1533cd454e6a7dc260d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
public import Mathlib.CategoryTheory.Shift.Opposite
public import Mathlib.CategoryTheory.Shift.Pullback
... |
11,429 | lean_file_chunk | 30bf852c8b3749592e84a7482dfe36dce1b461704b5e0c7a954d13c632258b09 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
module
public import Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated
public import Mathlib.CategoryTheory.Adjunction.Opposites
/-!
# Opposites of functors ... |
9,082 | lean_file_chunk | 281aed1ce9e15be3c6e6ccec2462d1eeb3d66dd7f33ba56e721203761f1d3dc6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Triangulated.Opposite.Triangle
public import Mathlib.CategoryTheory.Triangulated.HomologicalFunctor
/-!
# The pretriangulated stru... |
14,141 | lean_file_chunk | 0710a1abe72d0d4a848919ab2bf7f566b37b963266a8205c0d92e7dbda397ca8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
public import Mathlib.CategoryTheory.Triangulated.Triangulated
/-!
# Abelian subcategories of triangulated categorie... |
15,321 | lean_file_chunk | 48f5c48660674b8bbee54d0e34013b8d25b1e3aa48ad375e56643c143a10edee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE
/-!
# Truncations for a t-structure
Let `t` be a t-structure on a (pre)triangulated category `C... |
20,108 | lean_file_chunk | d591ae8f423aacbf8ddeed69adcdd20e8f59cbe4aea7ee1dfb8ba8d2c929d80b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT
public import Mathlib.Order.WithBotTop
/-!
# Truncations for a t-structure
Let `t` be a t-struc... |
3,299 | lean_file_chunk | 533b0d8d63ed5b3f6ce994134693fa7e89a4565879b656148bbbd160fc878cd9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
public import Mathlib.CategoryTheory.Triangulated.TStructure.Basic
/-!
# The heart of a t-structure
Let `t` be a t-... |
23,982 | lean_file_chunk | 2d435f9cd583ae96da759641356963123f884eec67a6b7ec2cba191c976c5231 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Triangulated.TStructure.Basic
public import Mathlib.CategoryTheory.Triangulated.Subcategory
/-!
# Truncations for a t-structure
L... |
14,057 | lean_file_chunk | f34d93e9973638baaa6c9aac4ad6645503c6dc7409fc3f21e5ebb2c0e95cb7f1 | lean_source_file | pkg_mathlib_source_file_chunks | t.liftTruncLT f n₀ n₁ h ≫ (t.truncLTι n₁).app Y = f :=
(t.liftTruncLT_aux f n₀ n₁ h).choose_spec.symm
end
section
variable {X Y : C} (f : X ⟶ Y) (n : ℤ) [t.IsGE Y n]
lemma descTruncGE_aux :
∃ (f' : (t.truncGE n).obj X ⟶ Y), f = (t.truncGEπ n).app X ≫ f' :=
Triangle.yoneda_exact₂ _ (t.triangleLTGE_distinguishe... |
10,355 | lean_file_chunk | 85a05e3371d0a8eb33bf5ed48d09cfcbdd2879fc0afdf0116a18fe0898deb3b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.CompleteLattice
public import Mathlib.CategoryTheory.ObjectProperty.Shift
public import Mathlib.CategoryTheory.Trian... |
7,110 | lean_file_chunk | 58c76cfc3eabf7357c43991b606e858f2682416f4d1b76fa37db7feeb91904a6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Triangulated.SpectralObject
public import Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc
/-!
# Spectral objects attached to... |
6,604 | lean_file_chunk | 50c5711ad3fe6e564442c3aee84b81f874c7504076611e9e1a342618d6a5d571 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.Shift
public import Mathlib.CategoryTheory.Triangulated.Subcategory
public import Mathlib.CategoryTheory.Triangulate... |
23,960 | lean_file_chunk | 2feae46cdb88426a00749dc9ed325e000b3c07231dd3d9e9a4986ac7ad716e5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Charlie Conneen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Charlie Conneen, Pablo Donato, Klaus Gy
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Balanced
pub... |
651 | lean_file_chunk | eb154adae7ddd155d888589365e1eb7222aab35c718f891d9f57fcf307b5e374 | lean_source_file | pkg_mathlib_source_file_chunks | apply ((𝒞₁.isPullback (e.inverse.map m)).map e.functor).of_iso (e.counitIso.app _)
(e.counitIso.app _) (.refl _) (.refl _) <;> simp
uniq {F G} m _ := by
intro χ₀' χ' hχ'
have : e.inverse.map χ' ≫ e.unitInv.app _ = 𝒞₁.χ (e.inverse.map m) := by
apply 𝒞₁.uniq (e.inverse.map m) (χ₀' := e.inverse.ma... |
10,768 | lean_file_chunk | ceda39267caa6755d2329c81303d27902fff0fcb4f86a51e5072f79b210ef5cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monad.Adjunction
public import Mathlib.CategoryTheory.Monad.Equalizer
/-!
# Adjoint lifting
This file gives two con... |
11,252 | lean_file_chunk | 9b27b4987017112dbed0544ada682eca8bc19a7a575e7ac12cb0072438396c46 | 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.CategoryTheory.Monad.Adjunction
public import Mathlib.CategoryTheory.Monad.Coequalizer
/-!
# Adjoint lifting
This file gives two construct... |
22,471 | lean_file_chunk | 0f6a9af2fb260c2f83919b0f7e0c73703c92305d5cc324c9d5c0c9002781b74c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Localization.Trifunctor
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Localization of monoidal cat... |
6,251 | lean_file_chunk | 0688ee8a64643d9b5c3312db12bbea8c88e422cb611637a7ef40cc9c5930d1dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Localization.Monoidal.Basic
public import Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor
/-!
# Localization o... |
7,015 | lean_file_chunk | 08ccdb8dd16f9b0be627c5feac9a391d98a6f9afbda2aa9d52bc0a4597770c1b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Localization.Trifunctor
public import Mathlib.CategoryTheory.Monoidal.Multifunctor
public import Mathlib.CategoryTheo... |
14,111 | lean_file_chunk | a4c48275bbe6438ffaa0ac04e32fe25c11c54852f301249a3bc7d78d8cf527f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions
public import Mathlib.CategoryTheor... |
2,042 | lean_file_chunk | 8af3a700a26fe974108f8644633f28c6bdd10b4ee33dac587832fa91633dfdff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.ComposableArrows.Basic
public import Mathlib.CategoryTheory.Localization.CalculusOfFractions
/-! # Essential surjecti... |
4,915 | lean_file_chunk | a451774fd7d2c6daf8f182620787698799544b29ecdd38201fee5ae19a98461b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Opposites
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Localizatio... |
9,896 | lean_file_chunk | b6a6e60445ea8012e4a8d3eeddcb008cf0272e31b48de53ce3cb2df05d7e14f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Localization.CalculusOfFractions
/-!
# Lemmas on fractions
Let `W : MorphismProperty C`, and objects `X` and `Y` in `C`. In this ... |
4,133 | lean_file_chunk | 0d1eab8840f3e2498e0f44fa1b25247b8562b744915169b137034876cab9313d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived
/-!
# Deriving functors using a derivability structure
Let `Φ : Localize... |
5,947 | lean_file_chunk | 6d60e3c53ef87b12ce98aa0705160a1b328fbdb635ebdfd67ae9ecf8183297f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic
/-!
# Constructor for derivability structures
In this file, we provide a constructor for... |
8,583 | lean_file_chunk | a474e8eb392e7a3194b9ec2ead7adc2ec9ee7104de8f0a0a7978a75dc1855c82 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Localization.Resolution
public import Mathlib.CategoryTheory.Localization.Opposite
public import Mathlib.CategoryTheory.GuitartExac... |
5,898 | lean_file_chunk | 17fd854983a29e28879ad380fa2a52dd6d9870c59e4e1ddcbc99a9703787a8fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic
public import Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived
public import M... |
4,888 | lean_file_chunk | cb60840a07d83be39dfca3521df0daf4ca8fcd66218a182a808081153a4cc977 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor
/-!
# Functorial resolutions give derivability structures
In this file, we provide... |
3,862 | lean_file_chunk | e707fb7b6ba78364d33128fd8ad74df2db42a1325c307a2605132e5340c9d705 | 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.Torsion
public import Mathlib.Data.ENat.Lattice
public import Mathlib.Data.ZMod.QuotientGroup
/-!
# Minimum order of an eleme... |
3,426 | lean_file_chunk | f971ae823a03635ad56adba7499a6e4fee50482bf9be396e90320ddccf16c826 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Kim Morrison
-/
module
public import Mathlib.GroupTheory.Coset.Basic
public import Mathlib.SetTheory.Cardinal.Finite
/-!
# Lagrange's theorem: the order of a subgro... |
22,221 | lean_file_chunk | 6942773b87a2a1adc6695774b7a8c70a3178c30a5f4435f805c89f38eaa769c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.Group.Subgroup.Basic
public import Mathlib.Data.S... |
9,208 | lean_file_chunk | b897aae8bb816c8d0b5ab1b7ccccc105d45e6fe49f1773be5206759e161e3eae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Kim Morrison
-/
module
public import Mathlib.Algebra.Quotient
public import Mathlib.Algebra.Group.Action.Opposite
public import Mathlib.Algebra.Group.Subgroup.MulOpp... |
3,775 | lean_file_chunk | 81bacac171b74fffb096b2e0a5036808d9e4d5030bc8a150e32f112e9d5390c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jordan Brown, Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jordan Brown, Thomas Browning, Patrick Lutz
-/
module
public import Mathlib.Algebra.Group.Subgroup.Finite
public import Mathlib.GroupTheory.Commutator.Bas... |
16,411 | lean_file_chunk | 5cd22a5616303b99cfaac0fc333194fce44218be35713d466e5217e7e0c997d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jordan Brown, Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jordan Brown, Thomas Browning, Patrick Lutz
-/
module
public import Mathlib.Algebra.Group.Commutator
public import Mathlib.GroupTheory.Subgroup.Centralize... |
1,096 | lean_file_chunk | d942820f0af86951ae5abd6219e75cd61ee57734e376f86aa640c7f0f2392989 | 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.ModEq
public import Mathlib.GroupTheory.QuotientGroup.Defs
public import Mathlib.Algebra.Group.Subgroup.ZPowers.Basic
/-!
# ... |
2,855 | lean_file_chunk | be22ee0c8e465e7a1b046f18b72d3423727f7c5d358644f5218e73148fc2521f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
-/
-- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
module
public import Mathlib.Algebra.Group.Subgr... |
19,966 | lean_file_chunk | 69e85cc207e602d12c463f18eca32646d4a4268a47dbae2d41f5336097b42551 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
-/
-- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
module
public import Mathlib.Algebra.Group.Subgr... |
16,530 | lean_file_chunk | 5faa742921b9da08a44dda2620f85eb997ff0748ac0047390c603fdb245c80da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
-/
-- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
module
public import Mathlib.Algebra.Group.Subgr... |
12,798 | lean_file_chunk | edb8b7fa76a07bb479ae814f7274c5377532522624daa653b49da298d0fe822b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Data.Finite.Sum
public import Mathlib.GroupTheory.OrderOfElement
public import Mathlib.GroupTheory.Perm.Support
public import Mathlib.Logic.... |
7,919 | lean_file_chunk | 1118424604c507d9112c5a8b288de24c83554b9f8c1b43c171eb6503a198e7b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Browning, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Junyan Xu
-/
module
public import Mathlib.Algebra.Group.Subgroup.Ker
public import Mathlib.GroupTheory.GroupAction.Basic
public import Mathlib.GroupTheory... |
21,006 | lean_file_chunk | 0c86eaa945bc2fcb1fb705f8f65342aad82547bdcbf60e720ee6d0e6400e235f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yi Yuan
-/
module
public import Mathlib.GroupTheory.Perm.Cycle.Type
public import Mathlib.GroupTheory.Perm.Option
public import Mathlib.Logic.Equiv.Fin.Rotate
/-!
# Permuta... |
23,988 | lean_file_chunk | 6c15e5498e7a5c164751941a4b20a2a9ff3a5261196219445eca3524b7618130 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.Group.Conj
public import Mathlib.Algebra.Group.Subgroup.Lattice
public import Mathlib.Algebra.Group.Submonoid.BigOperators
public im... |
2,815 | lean_file_chunk | 0943548f0a9f7a79f24dabb39494dc12e72cd32a2b508fcb13cf17664ab89143 | lean_source_file | pkg_mathlib_source_file_chunks | simp_rw [← fun a => sign_prodExtendRight a (σ a), Function.comp_def]
theorem sign_prodCongrLeft (σ : α → Perm β) : sign (prodCongrLeft σ) = ∏ k, sign (σ k) := by
refine (sign_eq_sign_of_equiv _ _ (prodComm β α) ?_).trans (sign_prodCongrRight σ)
rintro ⟨b, α⟩
rfl
@[simp]
theorem sign_permCongr (e : α ≃ β) (p : P... |
2,966 | lean_file_chunk | a6773277cccd15ba0a02e616c49c89e4b5abefcc7b89185aa2f87d56ecd2328c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Data.Fintype.Option
public import Mathlib.GroupTheory.Perm.Sign
/-!
# Permutations of `Option α`
-/
@[expose] public section
open Equiv
@... |
23,983 | lean_file_chunk | 2c2f6ed4dbbeebf868620822a70c8c37b149c17c03d627517321077ff2524a6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Aaron Anderson, Yakov Pechersky
-/
module
public import Mathlib.Algebra.Group.Commute.Basic
public import Mathlib.Algebra.Group.End
public import Mathlib.Data.Finset.Nonco... |
783 | lean_file_chunk | e9c6503b6fb6fc17465d3a1df3b68ac6ea5668f1bc6dcfab2f7607c48870385b | lean_source_file | pkg_mathlib_source_file_chunks | ### Fixed points
-/
variable {α : Type*}
theorem fixed_point_card_lt_of_ne_one [DecidableEq α] [Fintype α] {σ : Perm α} (h : σ ≠ 1) :
#{x | σ x = x} < Fintype.card α - 1 := by
rw [Nat.lt_sub_iff_add_lt, ← Nat.lt_sub_iff_add_lt', ← Finset.card_compl, Finset.compl_filter]
exact one_lt_card_support_of_ne_one h
... |
2,899 | lean_file_chunk | c83bb579cf03ec1329c56e9a8ad9b9bfe2bb5b0b8dc6ac14a681c6d0e444bee0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Finset
public import Mathlib.GroupTheory.Perm.Cycle.Factors
/-!
# Some lemmas pertaining t... |
14,253 | lean_file_chunk | e892ec83f75eb3324dd8942a7f3018bb414b5e643328c6479922ed198bf9c0b0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Order.Group.Nat
public import Mathlib.Data.List.Rotate
public import Mathlib.GroupTheory.Perm.Support
/-!
# Permutations from... |
4,610 | lean_file_chunk | 22de5c76f7d3b1eb7cd913e5a9878d45e1fa2c6c9b6dfae6f5cf4935e1d9240b | 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, Yaël Dillies
-/
module
public import Mathlib.GroupTheory.Perm.Cycle.Basic
/-!
# Closure results for permutation groups
* This file contains several closure results:
* `c... |
1,926 | lean_file_chunk | 4c1281d4653756b89a6bf9ef28e430d3b0cfdb2f440921ef2688b72a30727095 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.Action.Defs
public import Mathlib.Algebra.Group.End
public import Mathlib.Logic.Equiv.Set
public... |
15,447 | lean_file_chunk | a5fb2ed7ea24d6c2f4edb68ce68482f425937d6cc6aa3c90f6451a5efe5c86e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.Jordan
public import Mathlib.GroupTheory.SpecificGroups.Cyclic
public import Mathlib.GroupTheory.S... |
1,489 | lean_file_chunk | 46373511abdcb0f19b082577c01d209fae27e5d234111b02a815450f84ee1ec7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.End
public import Mathlib.Logic.Embedding.Basic
public import Mathlib.Logic.Equiv.Set
/-!
# `Eq... |
3,308 | lean_file_chunk | 641459db1025a0f46b27a3384396b4aad6c631b5a72f20eef53b4c40bd41846e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.Algebra.Group.Subgroup.Finite
public import Mathlib.Data.Fintype.Perm
/-!
# Lemmas about subgr... |
5,693 | lean_file_chunk | 03669decabb45ac702eaca07643693925d3d3cc3569666bec1e9b183119463f7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Junyan Xu, Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu, Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.Data.Fintype.Perm
public import Mathlib.Data.Set.Card... |
23,922 | lean_file_chunk | d0db34a07320b0a037ad9738538a8218c0bc45c381ca7f64d7ac3b3943a7e8fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public impo... |
7,393 | lean_file_chunk | 3f2bf0d9cf2cf16b629d68ea94647a6e450829651c99bd53010f13085a19612b | lean_source_file | pkg_mathlib_source_file_chunks | · exact Perm.ext fun x ↦ Subtype.ext (disjoint_iff_disjoint_support.mpr
((ofSubtype_support_disjoint a).mono_right
(mem_cycleFactorsFinset_support_le x.2))).commute.mul_inv_cancel
· intro i
refine ⟨⟨i, mem_centralizer_singleton_iff.mpr (self_mem_cycle_factors_commute i.2)⟩, ?_, rfl⟩
... |
13,373 | lean_file_chunk | 3ec831c56708af2cbe50fcfd50960e743afa2d40c93b47f658b6bb2fcfae80e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
module
public import Mathlib.Data.ZMod.Basic
public import Mathlib.GroupTheory.Coxeter.Basic
public import Mathlib.Tactic.Linarith
public import Mathlib.Tactic.Zify
/-!... |
8,406 | lean_file_chunk | a77f455127867a4882a97b819a28d208f9b24607d4b55c93abc5eae411a63d7e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen, Mitchell Lee
-/
module
public import Mathlib.LinearAlgebra.Matrix.Notation
public import Mathlib.LinearAlgebra.Matrix.Symmetric
/-!
# Coxeter matrices
Let us say that ... |
23,184 | lean_file_chunk | 1c77e760c82ebbf65255745db3bbeb30e3ce58953e95732a9354092e4330a653 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen, Mitchell Lee, Óscar Álvarez
-/
module
public import Mathlib.Algebra.Group.Subgroup.Pointwise
public import Mathlib.Algebra.Ring.Int.Parity
public import Mathlib.GroupThe... |
17,895 | lean_file_chunk | 96d7a4fee17c64ebc93b82b34d60fdac926964605a909269e74add217c45583d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee, Óscar Álvarez
-/
module
public import Mathlib.GroupTheory.Coxeter.Length
public import Mathlib.Data.List.GetD
public import Mathlib.Tactic.Group
/-!
# Reflections, invers... |
20,200 | lean_file_chunk | d8af57b30d87d205f447e3dbc5846ab54e4302ec504adc674ef233e92d7dbf86 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Subgroup.Actions
public import Mathlib.Algebra.Module.Defs
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Data.S... |
15,319 | lean_file_chunk | 7fa22f69cfe1fbf3e9a6fa95c6b8fbcd50cac8464b52dd179365c2176ad1e519 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.MultipleTransitivity
public import Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
... |
23,915 | lean_file_chunk | 6b387be52aa5b3d6b5a87eb1508eeda736eafda45cb0c3f845b1357b85110487 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.Primitive
public import Mathlib.GroupTheory.SpecificGroups.Alternating
public import Mathlib.Group... |
3,704 | lean_file_chunk | b58f5102b8fe8dd9461f7f74434bbbfbf842613b8caaf52451b35be1d0895ff5 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← Finset.notMem_compl, hs, Finset.mem_insert, Finset.mem_singleton, not_or] at h
simp [Equiv.swap_apply_of_ne_of_ne h.1 h.2, ← hg]
/-- A subgroup of `Equiv.Perm α` which is (card α - 2)-pretransitive
contains `alternatingGroup α`. -/
theorem _root_.IsMultiplyPretransitive.alternatingGroup_le
(G : Subgroup ... |
2,982 | lean_file_chunk | ad13492abaeb997b77be874d17bf0eb9a5d3a17dfdb3e5ce3280a71ac358f51b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.Defs
public import Mathlib.GroupTheory.GroupAction.Hom
/-! # Complements to pretransitive actions... |
20,731 | lean_file_chunk | 4d4c0c023352d2cd8c1bfdd54e37c735c4e9cb4b9a1b93db903c91f41c16174a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Pointwise.Set.Card
public import Mathlib.Data.Set.Card
public import Mathlib.GroupTheory.GroupAction.Multipl... |
1,696 | lean_file_chunk | eb456969934c67664813477cf1fe2f1594ac46b0e541f087e94c8e7dd461b2b3 | 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.Basic
public import Mathlib.Algebra.Group.Pointwise.Set.Scalar
/-!
# Support of an element under an action
Given an a... |
1,510 | lean_file_chunk | 677e3e77c2ccf842fe978b7324862f8571ee387c60e2eb9ecced5f6c7ebe0e44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Defs
public import Mathlib.Algebra.Ring.Defs
/-!
# Commutativity and associativity of action of integers on ring... |
9,850 | lean_file_chunk | 90fdf6bbf5d0745ce5a1aeea432a953122fd2db1f85c484c2c2d14372a50d4b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.GroupTheory.GroupAction.Defs
public import Mathlib.GroupTheory.Subgroup.Centralizer
/-!
# Conjugati... |
5,861 | lean_file_chunk | 4b624c8ec2b1a0a9c15f1de2d563ccaa81702d91591530602a6c4ef6d6c8f349 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen,
Frédéric Dupuis, Heather Macbeth, Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.P... |
15,022 | lean_file_chunk | f598cddbea4c8d68b543c59ccebe921091f6404b9352f68d2d560309b4baa217 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.Group.Action.Prod
publ... |
1,879 | lean_file_chunk | a9d5a32b484e3bbb9d6e5ed9e68b4782d41f809beddbb1f8603fa18998a82547 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.Action.Defs
public import Mathlib.Data.Countable.Defs
/-!
# Monoid action by iterates of a map
In this file we define ... |
21,323 | lean_file_chunk | 3c817d8038eaaeedd6a4f2c1dad0f1cf91d951bc76129deac51f15c14ce41585 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
module
public import Mathlib.Algebra.Group.Subgroup.Actions
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Dynamics.PeriodicPts.D... |
6,746 | lean_file_chunk | 504ce1270975c71254ba98230c912206021bf03ead1de633621cfda8c4bb0ea8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Subgroup.Lattice
public import Mathlib.GroupTheory.GroupAction.FixedPoints
/-!
# Fixing submonoid, fixing ... |
18,699 | lean_file_chunk | 1dbeadd9338a672daf8ffe5ccb23058fbbcb0c34693206e9a5c7390cf8f8ca78 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.Group.Action.Basic
public import Mathlib.Algebra.Group.Pointwise.Set.Scalar
public import Mathlib.Algebra.Group.Subgroup.Defs
public... |
1,873 | lean_file_chunk | 06cf2aaf916830aec551272700c8571524a0221f81e6557003ee7acaa64cc82b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bryan Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Wang
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.GroupTheory.GroupAction.SubMulAction
public import Mathlib.GroupTheory.QuotientGroup.Defs
/-!
# ... |
4,630 | lean_file_chunk | 4e2839dc1cf84a382fc271f7bbe10e29bb10d09afdc33b7c7aacf417f5561a15 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Emilie Burgun. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emilie Burgun
-/
module
public import Mathlib.Dynamics.PeriodicPts.Lemmas
public import Mathlib.GroupTheory.Exponent
public import Mathlib.GroupTheory.GroupAction.Basic
/-!
# Period o... |
1,926 | lean_file_chunk | 85b8a882072fc8c579556a9827b90ded19647d015984bf5dd44504b65d87f8e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Action.Basic
public import Mathlib.Algebra.Group.Action.Pi
public import Mathlib.Algebra.Group.Opposite
/-!
# Group actions on ... |
3,976 | lean_file_chunk | e8581eaa591aba8cb6f14a004fbd619319c69d4dfe0e6a6eb4e1e879caee5cb0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
module
public import Mathlib.Algebra.Group.ConjFinite
public import Mathlib.GroupTheory.Coset.Card
public import Mathlib.GroupTheory.GroupAction.Quotien... |
23,952 | lean_file_chunk | c8aa6f2faa4046cbe95e256c7b7e176f061be3cab864fa512cc27118472684d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Pointwise.Stabilizer
public import Mathlib.Data.Setoid.Partition
public import Mathlib.GroupTheory.GroupAction.Poi... |
6,455 | lean_file_chunk | e59f76f708cd4037f04a665262e47af5cd43f9c5c381d58b609c715a30a3f941 | lean_source_file | pkg_mathlib_source_file_chunks | obtain ⟨k, rfl⟩ := htGX.exists_smul_eq a b
suffices k ∈ stabilizer G B' by
exact this.symm ▸ (Set.smul_mem_smul_set ha')
exact hBB' (hB.smul_eq_of_mem ha hb)
· intro hBB' g hgB
apply hB'.smul_eq_of_mem ha'
exact hBB' <| hgB.symm ▸ (Set.smul_mem_smul_set ha)
/-- The type of blocks fo... |
3,651 | lean_file_chunk | c9d79e3416d3e01de3316077da427aface12c2f92e2169c0cc1fd8015caa3cb8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.GroupTheory.GroupAction.Primitive
public import Mathlib.GroupTheory.Subgrou... |
11,493 | lean_file_chunk | b02c3a8f2655457e82551d1c5246e9f84823d9a9627fdc27f8eb855546235100 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Emilie Burgun. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emilie Burgun
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.Group.Commute.Basic
public import Mathlib.Dynamics.PeriodicPts.Defs... |
16,354 | lean_file_chunk | 30b133642babbe39946f0a36ba26773e932eca4bd4dfce2eb18c0649f905d51d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.BigOperators.Finprod
public import Mathlib.Data.Nat.Prime.Basic
public import Mathlib.Data.Setoid.Partition.Card
p... |
23,972 | lean_file_chunk | d2bff089e0dcefc606a32213f046b3b022a12ba0ec6d0b64f14d130dfb87e1c4 | 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, Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Hom.CompTypeclasses
public import Mathlib.Algebra.Module.Defs
public import Mathlib.Algebra.Notation.Prod
pub... |
14,548 | lean_file_chunk | a0b400bb1785624ddc9a9528010a79c597996ee440787fc4fe82c9d609f6521a | lean_source_file | pkg_mathlib_source_file_chunks | /-- `DistribMulActionHomClass F M A B` states that `F` is a type of morphisms preserving
the additive monoid structure and equivariant with respect to the action of `M`.
It is an abbreviation to `DistribMulActionHomClass F (MonoidHom.id M) A B`
You should extend this class when you extend `DistribMulActionHom`. -/]
abb... |
23,984 | lean_file_chunk | 4aa89a26007835a07ed3e266df9156bf939795f28a0169c446e9dcbbb64d82b0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.PUnit
public import Mathlib.Algebra.Group.Subgroup.Ker
public import Mathlib.Algebra.Group.Submonoid.Membership
public i... |
4,344 | lean_file_chunk | cfe08c3e8fe2addbc16aef4a38b9a0f57e887e25cfec3fc62d9fdcea6208de32 | lean_source_file | pkg_mathlib_source_file_chunks | @[to_additive]
instance : Group (G ∗ H) where
inv_mul_cancel := mk_surjective.forall.2 fun x => mk_eq_mk.2 (con_inv_mul_cancel x)
@[to_additive (attr := simp)]
theorem closure_range_inl_union_inr :
Subgroup.closure (range (inl : G →* G ∗ H) ∪ range inr) = ⊤ :=
Subgroup.closure_eq_top_of_mclosure_eq_top mclosur... |
603 | lean_file_chunk | af18527697876c417cb99a3c0f8233ee3b327fc1654bce0422bdf23c1dfb3431 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Michael Howes, Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.Abelianization.Defs
public import Mathlib.GroupTheory.Coset.Card
/-!
# The abelianization of a ... |
6,294 | lean_file_chunk | d433cc3fd82b525f66a152ab2f44a4e70952d4d57e8f98200a5d92833df45be3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Michael Howes, Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.Commutator.Basic
/-!
# The abelianization of a group
This file defines the commutator and the ... |
7,110 | lean_file_chunk | 38cf030a5ef660b728c59a74da99aeca29f0a28d8e1974d4dc2680f0e88cd4a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Group.Submonoid.Pointwise
/-!
# Submonoid of inverses
Given a submonoid `N` of a monoid `M`, we define the submonoid `N.leftInv` as... |
7,124 | lean_file_chunk | f8c9d8bbcc4d10617e105f2e102b664a7a3aec0ba0a8bf21b4c80c491500a7ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Submonoid.Operations
public import Mathlib.GroupTheory.Subsemigroup.Center
/-!
# Centers of monoids
## Main definitions
* `Su... |
3,957 | lean_file_chunk | 29c523c759faaf3826cc6f5696651d5eb9f57dea16a0c26c02b18389ca99b9b2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.GroupTheory.Subsemigroup.Centralizer
public import Mathlib.GroupTheory.Submonoid.Center
/-!
# Centralizers of magmas and monoids
## ... |
9,249 | lean_file_chunk | 5a0fc2f6974b25df7689d81816989184cc54d586151f25e2d3eb29ebf96b0315 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.GroupTheory.FiniteAbelian.Basic
public import Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity
/-!
# Duality for finite abelian groups
... |
11,155 | lean_file_chunk | aa4da3b7b55666de450ecd332672c446c9f89c9770f43e2988c371878d00a0ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-/
module
public import Mathlib.Algebra.Module.PID
public import Mathlib.Algebra.Group.TypeTags.Finite
public import Mathlib.Data.ZMod.QuotientRing
/-!... |
1,800 | lean_file_chunk | dcb4894e5c4b755758a03640ce3005778f8ad3cea356f8a5cb023c1723e55c7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Opposites
public import Mathlib.GroupTheory.Congruence.Defs
/-!
# Congruences on the opposite of a group
This file defin... |
14,312 | lean_file_chunk | 840d5e61b44e4590506f7de9eb4b6ba6f20ba07ecf06f71ca4a475a53cc14269 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Group.Submonoid.Operations
public import Mathlib.Data.Setoid.Basic
public import Mathlib.GroupTheory.Congruence.Hom
/-!
#... |
23,981 | lean_file_chunk | a91cb1b303a66c6b898fdce11f277eb57c9bf68a6144832df0674a2fe6a5e93f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Group.InjSurj
public import Mathlib.Algebra.Group.Units.Defs
public import Mathlib.Data.Setoid.Basic
public import Mathlib... |
10,003 | lean_file_chunk | 73095a839375f2e836a15faf0e982d94fbc7c256036452b8f9da431c57a31df8 | lean_source_file | pkg_mathlib_source_file_chunks | /-- The 1 of the quotient of a monoid by a congruence relation is the equivalence class of the
monoid's 1. -/
@[to_additive (attr := simp) /-- The 0 of the quotient of an `AddMonoid` by an additive congruence
relation is the equivalence class of the `AddMonoid`'s 0. -/]
theorem coe_one : ((1 : M) : c.Quotient) = 1 :=
... |
1,801 | lean_file_chunk | 4e5cca87c6b861f5db9ab0845aa3e9cc63923f435642d8381a1848da421d6d96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
public import Mathlib.Algebra.BigOperators.Group.List.Lemmas
public import Mathlib.Group... |
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