filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
path.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(******************************************************************************)
(* ... |
inertia.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype div... |
LowDegree.lean | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
import Mathlib.GroupTheory.Abelianization.Defs
import Mathlib.RepresentationTheory.Homological.GroupHomol... |
Basic.lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Algebra.Order.Sub.Unbundled.Basic
impor... |
KleinFour.lean | /-
Copyright (c) 2023 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
/-!
# Klein Four Group
The Klein (Vierergruppe) four-group is a non-cyclic abelian group with four elements, in which... |
CanonicalBilinear.lean | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.Algebra.Ring.SumsOfSquares
import Mathlib.LinearAlgebra.RootSystem.RootPositive
/-!
# The canonical bilinear form on a finite root pairing
Given a fin... |
SetLike.lean | /-
Copyright (c) 2024 Sven Manthe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sven Manthe
-/
import Mathlib.Order.CompleteSublattice
/-!
# `SetLike` instance for elements of `CompleteSublattice (Set X)`
This file provides lemmas for the `SetLike` instance for ele... |
Inverse.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import Mathlib.Algebra.Group.Units.Basic
import Mathlib.RingTheory.MvPowerSeries.Basic
import Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors
import Mathl... |
check-yaml.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Lean.Util.SearchPath
import Mathlib.Lean.CoreM
import Mathlib.Tactic.ToExpr
/-! # Script to check `undergrad.yaml`, `overview.yaml`, `100.yaml` and `1000.yaml`
Thi... |
Pi.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Data.Multiset.Bind
/-!
# The cartesian product of multisets
## Main definitions
* `Multiset.pi`: Cartesian product of multisets indexed by a multise... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
Zero.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal
import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
/-!
# Preservation of zero objects and zero mo... |
Defs.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.SetNotation
import Mathlib.Order.WellFounded
/-!
# Definitions of conditionally complete lattices
A con... |
Products.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# (Co)products in functor categories
Given `f : α ... |
Basic.lean | /-
Copyright (c) 2024 Judith Ludwig, Florent Schaffhauser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Judith Ludwig, Florent Schaffhauser, Yunzhou Xie, Jujian Zhang
-/
import Mathlib.LinearAlgebra.TensorProduct.Quotient
import Mathlib.RingTheory.Flat.Stability
/-!... |
Equivs.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.DualNumber
import Mathlib.Algebra.QuaternionBasis
import Mathlib.Data.Complex.Module
import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
import ... |
Sl2.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
/-!
# The Lie algebra `... |
LiouvilleNumber.lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Jujian Zhang
-/
import Mathlib.NumberTheory.Transcendental.Liouville.Basic
/-!
# Liouville constants
This file contains a construction of a family of Liouville numbers,... |
UnifTight.lean | /-
Copyright (c) 2023 Igor Khavkine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Igor Khavkine
-/
import Mathlib.MeasureTheory.Function.ConvergenceInMeasure
import Mathlib.MeasureTheory.Function.UniformIntegrable
/-!
# Uniform tightness
This file contains the defi... |
Basic.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact
import Mathlib.AlgebraicGeometry.Properties
/-!
# Ideal sheaves on schemes
We define ideal sheaves of schemes and ... |
HomLift.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.CommSq
/-!
# HomLift
Given a functor `p : 𝒳 ⥤ 𝒮`, this file provides API for... |
morphism.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype finfun bigop finset fingroup.
(***********... |
Free.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Star.Basic
import Mathlib.Algebra.FreeAlgebra
/-!
# A *-algebra structure on the free algebra.
Reversing words gives a *-structure on the free mono... |
Subgroup.lean | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.GroupWithZero.Subgroup
import Mathlib.Algebra.Ring.Submonoid.Pointwise
import Mathlib.Algebra.Module.Defs
/-!
# Additive subgroups of rings
-/
open sco... |
IntegralRNDeriv.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Analysis.Convex.Continuous
import Mathlib.Analysis.Convex.Integral
import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym
/-!
#... |
NAry.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Lattice.Prod
import Mathlib.Data.Finite.Prod
import Mathlib.Data.Set.Lattice.Image
/-!
# N-ary images of finsets
This file defines `Finset.im... |
poly.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop fi... |
FunctorCategory.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Preadditive.FunctorCategory
import Mathlib.CategoryTheory.Linear.Basic
/-!
# Linear structure on functor categories
If `C` and `D` are cat... |
PUnit.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Group.Defs
/-!
# `PUnit` is a commutative group
This file collects facts about algebraic structures on the one-element type, e.g. that it is a
commutat... |
IsolatedZeros.lean | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
import Mathlib.Analysis.Meromorphic.Basic
/-!
# Principles of Isolated Zeros and Identity Principles for Meromorphic Functions
In line with results in `Mathlib.Anal... |
Defs.lean | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Init.Data.ULift
import Init.Data.Fin.Fold
import Init.Data.List.Nat.Pairwise
import Init.Data.List.Nat.Range
import Mathlib.NumberTheory.NumberField.Basic
import... |
generic_quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice.
From mathcomp Require Import seq fintype.
(*****... |
ProfiniteGrp.lean | import Mathlib
universe v u
open CategoryTheory ProfiniteGrp
set_option maxHeartbeats 10000
set_option synthInstance.maxHeartbeats 2000
variable {X Y Z : Type u} [Group X] [TopologicalSpace X] [IsTopologicalGroup X]
[CompactSpace X] [TotallyDisconnectedSpace X] [Group Y] [TopologicalSpace Y]
[IsTopologicalG... |
ValuativeCriterion.lean | /-
Copyright (c) 2024 Andrew Yang, Qi Ge, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Qi Ge, Christian Merten
-/
import Mathlib.AlgebraicGeometry.Morphisms.Immersion
import Mathlib.AlgebraicGeometry.Morphisms.Proper
import Mathlib.Ring... |
Pretransitive.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.TypeTags
/-!
# Pretransitive group actions
This file defines a typeclass for pretransitive group actions.
## Notat... |
ProjectiveSeminorm.lean | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
import Mathlib.Analysis.NormedSpace.Multilinear.Basic
import Mathlib.LinearAlgebra.PiTensorProduct
/-!
# Projective seminorm on the tensor of a finite family of normed s... |
finmodule.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
Extension.lean | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Basic
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
/-!
# Extensions and lifts in bicategories
We introduce the conce... |
integral_char.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
Type.lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.GCDMonoid.Multiset
import Mathlib.Algebra.GCDMonoid.Nat
import Mathlib.Algebra.Group.TypeTags.Finite
import Mathlib.Combinatorics.Enumerative... |
Basic.lean | /-
Copyright (c) 2025 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.Algebra.GroupWithZero.Range
import Mathlib.Algebra.Order.Group.Cyclic
impor... |
Monotone.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import Mathlib.Tactic.Order
import Mathlib.Topology.Order.IsLUB
/-!
# Monotone functions on an order topology
This file contains le... |
Basic.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Group.Submonoid.BigOperators
import Mathlib.GroupTheory.Subsemigroup.Center
import Mathlib.RingTheory... |
sylow.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import fintype prime bigop finset fingroup morphism.
From mat... |
Basic.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.MetricSpace.Basic
/-!
# Metrizability of a T₃ topological space with second countable topology
In this file we define metrizable topologic... |
Faithful.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Faithful
import Mathlib.Algebra.GroupWithZero.NeZero
/-!
# Faithful actions involving groups with zero
-/
assert_no... |
WalkDecomp.lean | /-
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
-/
import Mathlib.Combinatorics.SimpleGraph.Walk
/-!
# Decomposing walks
## Main definitions
- `takeUntil`: The path obtained by taking edges of an existing path u... |
OrderIso.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Algebra.Group.Units.Equiv
import Mathlib.Algebra.Order.Group.Unbundled.Basic
import Mathlib.Order.Hom.... |
Sequence.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Compactification.OnePoint.Basic
import Mathlib.Topology.Category.LightProfinite.Basic
/-!
# The light profinite set classifying convergen... |
Sign.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.Sign.Defs
import Mathlib.Topology.Order.Basic
/-!
# Topology on `SignType`
This file gives `SignType` the discrete topology, and proves continuity r... |
PiProd.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# A product as a binary product
We write a p... |
Diam.lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import Mathlib.Topology.EMetricSpace.Pi
/-!
# Diameters of sets in extended metric spaces
-/... |
Resolution.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Kim Morrison, Joël Riou
-/
import Mathlib.Algebra.Homology.QuasiIso
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
import Mathlib.Algebra.Homology.SingleHo... |
Clear_.lean | /-
Copyright (c) 2022 Joshua Clune. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joshua Clune
-/
import Mathlib.Init
import Lean.Meta.Tactic.Clear
import Lean.Elab.Tactic.Basic
/-! # `clear_` tactic -/
namespace Mathlib.Tactic
open Lean Meta Elab.Tactic
/-- Clear ... |
Core.lean | /-
Copyright (c) 2022 Mario Carneiro, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth, Yaël Dillies
-/
import Mathlib.Tactic.NormNum.Core
import Mathlib.Tactic.HaveI
import Mathlib.Algebra.Order.Invertible
import Mathlib.... |
inequalities.lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Tactic.Linarit... |
Norm.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Real.Sqrt
/-!
# Norm on the complex numbers
-/
noncomputabl... |
Cotangent.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Exp
import Mathlib.Analysis.Complex.IntegerCompl
import Mathlib.Analysis.Complex.LocallyUniformLimit
import Mathlib.Ana... |
bound.lean | /-
Copyright (c) 2024 Geoffrey Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Geoffrey Irving
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Tactic.Bound
/-!
## Tests for the `bound` tactic
-/
open Complex (abs)
open scoped NNReal
-- Te... |
ULiftable.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Monad.Basic
import Mathlib.Control.Monad.Cont
import Mathlib.Control.Monad.Writer
import Mathlib.Logic.Equiv.Basic
import Mathlib.Logic.Equiv.Functor... |
Field.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Order.Filter.AtTopBot.Ring
/-!
# Convergence to ±infinity in linear ordered (semi)fields
-/
namespace Filter
var... |
intdiv.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
DeltaGeneratedSpace.lean | /-
Copyright (c) 2024 Ben Eltschig. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ben Eltschig
-/
import Mathlib.Analysis.LocallyConvex.WithSeminorms
/-!
# Delta-generated topological spaces
This file defines delta-generated spaces, as topological spaces whose topol... |
Basic.lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
import Mathlib.Dynamics.FixedPoints.Basic
import Mathlib.GroupTheory.Perm.Option
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Equiv.Option
import Mathlib.Tactic... |
Units.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Faithful
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Units.Defs
/-! # Group actions on and by `Mˣ`
This file provi... |
Group.lean | import Mathlib.Tactic.Group
variable {G : Type} [Group G]
example (a b c : G) : c*(a*b)*(b⁻¹*a⁻¹)*c = c*c := by group
example (a b c : G) : (b*c⁻¹)*c*(a*b)*(b⁻¹*a⁻¹)*c = b*c := by group
example (a b c : G) : c⁻¹*(b*c⁻¹)*c*(a*b)*(b⁻¹*a⁻¹*b⁻¹)*c = 1 := by group
-- The following is known as the Hall-Witt identity,
--... |
Basic.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Set.Lattice
import Mathlib.Order.ConditionallyCompleteLattice.Defs
/-!
# Theory of conditionally complete lattices
A conditionally complet... |
OpClass.lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Init
/-!
# Typeclasses for commuting heterogeneous operations
The three classes in this file are for two-argument functions where one inpu... |
tuple.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat.
From mathcomp Require Import seq choice fintype path.
S... |
sesquilinear.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup.
From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector.
(************************************************... |
Lattice.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn, Yaël Dillies
-/
import Mathlib.Algebra.Group.Pointwise.Set.Scalar
import Mathlib.Data.Set.Lattice.Image
import Mathlib.Algebra.Group.Pointwise.Set.Bas... |
Faithful.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Defs
/-!
# Faithful group actions
This file provides typeclasses for faithful actions.
## Notation
- `a • b` is u... |
Whiskering.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Sheaf
/-!
In this file we construct the functor `Sheaf J A ⥤ Sheaf J B` between sheaf categories
obtained by composition with a functor ... |
UniformOn.lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Bhavik Mehta
-/
import Mathlib.Probability.ConditionalProbability
import Mathlib.MeasureTheory.Measure.Count
/-!
# Classical probability
The classical formulation of probab... |
Presheaf.lean | /-
Copyright (c) 2025 Pablo Donato. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pablo Donato
-/
import Mathlib.CategoryTheory.Subobject.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Subobjects presheaf
Following Section I.3 of [Sheav... |
AEEqOfLIntegral.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.StronglyMeasurable.ENNReal
import Mathlib.MeasureTheory.Measure.WithDensity
/-! # From equality of integrals to equality of functio... |
AEEqFun.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.MeasureTheory.Function.L1Space.Integrable
/-!
# `L¹` space
In this file we establish an API between `Integrable` and the space `L¹` of equivalence
clas... |
all_field.v | From mathcomp Require Export algC.
From mathcomp Require Export algebraics_fundamentals.
From mathcomp Require Export algnum.
From mathcomp Require Export closed_field.
From mathcomp Require Export cyclotomic.
From mathcomp Require Export falgebra.
From mathcomp Require Export fieldext.
From mathcomp Require Export fin... |
Comp.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.PFunctor.Multivariate.Basic
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The composition of QPFs is itself a QPF
We define compos... |
SimplexAlgorithm.lean | /-
Copyright (c) 2024 Vasily Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasily Nesterov
-/
import Mathlib.Tactic.Linarith.Datatypes
import Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.PositiveVector
/-!
# The oracle based on Simplex Algorithm
This fi... |
Extreme.lean | /-
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
-/
import Mathlib.Analysis.Convex.Hull
/-!
# Extreme sets
This file defines extreme sets and extreme points for sets in a module.
An extreme s... |
LinearMap.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# Cayley-Hamilton theorem for f.g. modules.
Given a fixed finite spannin... |
Membership.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Group.Subsemigroup.Basic
/-!
# Subsemigroups: membership criteria
In this file we prove various facts about membership in a subsemigroup.
The i... |
Braided.lean | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
import Mathlib.CategoryTheory.Monoidal.DayConvolution
/-!
# Braidings for Day convolution
In this file, we show that if `C` is a braided monoidal category and
`V` als... |
Measure.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
import Mathlib.NumberTheory.Transcendental.Liouville.Residual
import Mathlib.NumberTheory.Transcendental.Liouvil... |
UrysohnsBounded.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.UrysohnsLemma
import Mathlib.Topology.ContinuousMap.Bounded.Basic
/-!
# Urysohn's lemma for bounded continuous functions
In this file we r... |
Lex.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Logic.Function.Defs
import Mathlib.Order.Defs.Unbundled
/-!
# Lexicographic order on a sigma type
This defines the lexicographical order of two arbitrary... |
FiniteExtension.lean | /-
Copyright (c) 2025 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import Mathlib.Analysis.Normed.Unbundled.AlgebraNorm
import Mathlib.Analysis.Normed.Unbundled.SeminormFromBounded
import Mathlib.Analy... |
Units.lean | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching, Ashvni Narayanan, Michael Stoll
-/
import Mathlib.Algebra.BigOperators.Associated
import Mathlib.Data.ZMod.Basic
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# Lem... |
Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.Group.Action.Faithful
import Mathlib.Algebra.Group.Pi.Basic
import Mathlib.Data.Set.Piecewise
/-!
# Pi instances for multiplicative ... |
CubicDiscriminant.lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.Algebra.Polynomial.Splits
import Mathlib.Tactic.IntervalCases
/-!
# Cubics and discriminants
This file defines cubic polynomials ... |
Defs.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.SetNotation
/-!
# Definition of complete lattices
This file contains the definition of complete lattices with... |
Result.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Archive.Examples.IfNormalization.Statement
import Mathlib.Data.List.AList
import Mathlib.Tactic.Recall
/-!
# A solution to the if normalization challenge in Lean.... |
Nondegenerate.lean | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.LinearAlgebra.BilinearForm.Basic
import Mathlib.LinearAlgebra.BilinearForm.Orthogonal
import Mathlib.LinearAlgebra.Dimension.Localization
import Mathli... |
GrothendieckGroup.lean | /-
Copyright (c) 2025 Alex J. Best, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Yaël Dillies
-/
import Mathlib.GroupTheory.MonoidLocalization.Basic
/-!
# Grothendieck group
The Grothendieck group of a commutative monoid `M` is the "smal... |
Representable.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Joël Riou, Ravi Vakil
-/
import Mathlib.CategoryTheory.MorphismProperty.Limits
/-!
# Relatively representable morphisms
In this file we define and develop basic results a... |
cyclotomic.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype tuple finfun bigop prime.
From mat... |
cyclotomic.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype tuple finfun bigop prime.
From mat... |
Basic.lean | /-
Copyright (c) 2020 Anne Baanen. 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
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.... |
EffectiveEpi.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
import Mathlib.Topology.Category.CompHaus.Limits
import Mathlib.Topology.Category.CompHausLike.EffectiveEpi
/-!
# Effective epimorphisms in `CompHaus`
Thi... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.