filename stringlengths 5 42 | content stringlengths 15 319k |
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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.
(***********... |
Over.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Comma.Over.Basic
import Mathlib.CategoryTheory.Limits.Comma
import Mathlib.CategoryTheory.Limits.ConeCategory... |
EuclideanDist.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.Analysis.InnerProductSpace.Calculus
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Topology.MetricSpace.ProperSpace.Lemmas
/-!
# Eucl... |
Basic.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Logic.Equiv.Defs
/-!
# Monad
## Attributes
* ext
* functor_norm
* monad_norm
## Implementation Details
Set of rewrite rules and automation for monads in... |
Equiv.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton,
Anatole Dedecker
-/
import Mathlib.Logic.Equiv.Fin.Basic
import Mathlib.Topology.UniformSpace.UniformEm... |
finfun.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 choice.
From mathcomp Require Import fintype tuple.
... |
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... |
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... |
EquivFunctor.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Convert
/-!
# Functions functorial with respect to equivalences
An `EquivFunctor` is a function from `Type → Type`... |
gproduct.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 div.
From mathcomp Require Import choice fintype bigo... |
InitialSeg.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-/
import Mathlib.Data.Sum.Order
import Mathlib.Order.Hom.Lex
import Mathlib.Order.RelIso.Set
import Mathlib.Order.UpperLow... |
Hom.lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Floris van Doorn
-/
import Mathlib.Topology.VectorBundle.Basic
/-!
# The vector bundle of continuous (semi)linear maps
We define the (topological) vector bundle of ... |
Finite.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.Algebra.Group.AddChar
import Mathlib.Algebra.Group.TypeTags.Finite
import Mathlib.Analysis.No... |
FiniteType.lean | /-
Copyright (c) 2025 Christian Merten, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten, Andrew Yang
-/
import Mathlib.Algebra.Category.CommAlgCat.Basic
import Mathlib.CategoryTheory.MorphismProperty.Comma
import Mathlib.RingTheory.FinitePr... |
Basic.lean | /-
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
-/
import Mathlib.Algebra.Module.PID
import Mathlib.Algebra.Group.TypeTags.Finite
import Mathlib.Data.ZMod.QuotientRing
/-!
# Structure of finite(ly gen... |
Real.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
-/
import Mathlib.Topology.Metrizable.Basic
import Mathlib.Topology.Order.MonotoneContinuity
import Mathlib.Topology.Order.Real
/-!
# `ENNReal` is metri... |
RankAndCardinality.lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.FieldTheory.IntermediateField.Adjoin.Basic
import Mathlib.FieldTheory.MvRatFunc.Rank
import Mathlib.RingTheory.Algebraic.Cardinality
import Mathlib.RingThe... |
Prod.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Algebra.Algebra.Hom
import Mathlib.Algebra.Module.Prod
/-!
# The R-algebra structure on products of R-alge... |
alt.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 div fintype tupl... |
Trunc.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.RingTheory.MvPowerSeries.Basic
import Mathlib.Data.Finsupp.Interval
import Mathlib.Algebra.MvPolynomial.Eval
/-!
# Formal (multivariate) ... |
Matrix.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.AffineSpace.Basis
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
# Matrix results for barycentric co-ordinates
Results about the ... |
bigop.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 fintype tuple ... |
CentroidHom.lean | /-
Copyright (c) 2024 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Algebra.Ring.CentroidHom
import Mathlib.Algebra.Star.StarRingHom
import Mathlib.Algebra.Star.Subsemiring
import Mathlib.Algebra.Star.Basic
/-... |
Lemmas.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.Topology.GDelta.Basic
/-!
# Baire spaces
A topological space is called a *Baire space*
if a countable intersection of dense open subsets is den... |
PropEncodable.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Data.W.Basic
import Mathlib.Data.Fin.VecNotation
/-!
# W types
The file `Mathlib/Data/W/Basic.lean` shows that if `α` is an encodable fintype and for e... |
NonZeroDivisors.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma, Oliver Nash
-/
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.GroupWithZero.Associated
import Mathlib.Algebra.GroupWithZero.Regular
import M... |
Opposite.lean | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Abelian.Yoneda
import Mathlib.CategoryTheory.Generator.Abelian
import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives... |
Epi.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.SequentialProduct
import Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit
import Mathlib.Condensed.Light.Limits
/... |
Subring.lean | /-
Copyright (c) 2025 Michal Staromiejski. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michal Staromiejski
-/
import Mathlib.Algebra.Ring.Subsemiring.Basic
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.RingTheory.LocalRing.Defs
/-!
# Subrings ... |
Defs.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Yury Kudryashov
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Order.TypeTags
/-! # Definition and notation for extended natural numbers -/
/-- Exte... |
Ideal.lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma, Wojciech Nawrocki
-/
import Mathlib.RingTheory.Ideal.IsPrimary
import Mathlib.RingTheory.Ideal.Quotient.Operations
import Mathlib.RingTheory.TwoSidedIdeal.Operations... |
Int.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Algebra.Module.LocalizedModule.Basic
import Mathlib.Algebra.Module.Submodule.Pointwise
/-!
# Integer elements of a localized module
This is a mi... |
docs.lean | import docs.Conv.Guide
import docs.Conv.Introduction
|
Prespectral.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.Order.Ideal
import Mathlib.Topology.Sets.Compacts
import Mathlib.Topology.Sets.OpenCover
import Mathlib.Topology.Spectral.Hom
/-!
# Prespectral spaces
In ... |
Exponential.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-/
import Mathlib.SetTheory.Ordinal.Family
/-! # Ordinal exponential
In this file we define the power function and the lo... |
Exponential.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.Order.CauSeq.BigOperators
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Data.C... |
Injective.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.Category.ModuleCat.EpiMono
import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
import Mathlib.Algebra.EuclideanDomain.Int
import Mathlib.Algebra... |
Circumcenter.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Geometry.Euclidean.Projection
import Mathlib.Geometry.Euclidean.Sphere.Basic
import Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid
import Mathlib.Linea... |
EquationalCriterion.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee, Junyan Xu
-/
import Mathlib.RingTheory.Flat.Basic
import Mathlib.LinearAlgebra.TensorProduct.Vanishing
import Mathlib.Algebra.Module.FinitePresentation
/-! # The equationa... |
Uniformity.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Nat.Lattice
import Mathlib.Data.NNReal.Basic
import Mathlib.Topology.Metrizable.Basic
/-!
# Metrizable uniform spaces
In this file we prove th... |
Character.lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.RepresentationTheory.FDRep
import Mathlib.LinearAlgebra.Trace
import Mathlib.RepresentationTheory.Invariants
/-!
# Characters of representations
Th... |
Bifunctor.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.TotalComplex
import Mathlib.CategoryTheory.GradedObject.Bifunctor
/-!
# The action of a bifunctor on homological complexes
Given a bifunctor `... |
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.
(******************************************************************************)
(* ... |
ModEq.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.NoZeroSMulDivisors.Basic
import Mathlib.Data.Int.ModEq
import Mathlib.GroupTheory.QuotientGroup.Defs
import Math... |
NeZero.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import Mathlib.Data.Nat.Cast.Defs
/-!
# Lemmas about nonzero elements of an `AddMonoidWithOne`
-/
open Nat
namespace NeZero
theorem one_le {n : ℕ} ... |
Finsupp.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Algebra.BigOperators.Finsupp.Basic
/-! # Connection between `Submonoid.closure` and `Finsupp.prod` -/
assert_not_exists Field
namespace Submonoid
variabl... |
Zero.lean | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.LinearAlgebra.Charpoly.ToMatrix
import Mathlib.LinearAlgebra.Determinant
import Mathlib.LinearAlgebra.Ei... |
VolumeOfBalls.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 Mathlib.Data.Complex.FiniteDimensional
import Mathlib.MeasureTheory.Constructions.HaarToSphere
import Mathlib.MeasureTheory.Integral.Gamma
import Mathlib.Measure... |
Exact.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Jujian Zhang
-/
import Mathlib.Algebra.Exact
import Mathlib.Algebra.Module.LocalizedModule.Basic
/-!
# Localization of modules is an exact functor
## Main definitions
- `... |
Galois.lean | /-
Copyright (c) 2024 Yongle Hu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yongle Hu, Jiedong Jiang
-/
import Mathlib.NumberTheory.RamificationInertia.Basic
import Mathlib.RingTheory.Invariant.Basic
/-!
# Ramification theory in Galois extensions of Dedekind domai... |
Perfect.lean | /-
Copyright (c) 2022 Felix Weilacher. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Felix Weilacher
-/
import Mathlib.Topology.Perfect
import Mathlib.Topology.MetricSpace.Polish
import Mathlib.Topology.MetricSpace.CantorScheme
import Mathlib.Topology.Metrizable.Real... |
finalg.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 choice.
From mathcomp Require Import fintype finset f... |
Basic.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.FreeAlgebra
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Algebra.Category.ModuleCat.Ba... |
ConcreteCategory.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.HomologySequence
import Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory
/-!
# Homology of complexes in concrete categories
The homology... |
Nth.lean | /-
Copyright (c) 2021 Vladimir Goryachev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Vladimir Goryachev, Kyle Miller, Kim Morrison, Eric Rodriguez
-/
import Mathlib.Data.List.GetD
import Mathlib.Data.Nat.Count
import Mathlib.Data.Nat.SuccPred
import M... |
DualNumber.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.TrivSqZeroExt
/-!
# Dual numbers
The dual numbers over `R` are of the form `a + bε`, where `a` and `b` are typically elements of a
commutative ring... |
Sequence.lean | /-
Copyright (c) 2025 Julian Berman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Hill, Julian Berman, Austin Letson, Matej Penciak
-/
import Mathlib.Algebra.Polynomial.Monic
import Mathlib.LinearAlgebra.Basis.Basic
/-!
# Polynomial sequences
We define polyn... |
Finite.lean | /-
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
-/
import Mathlib.GroupTheory.Abelianization.Defs
import Mathlib.GroupTheory.Coset.Card
/-!
# The abelianization of a finite group is finite... |
Flag.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
import Mathlib.Algebra.Order.Group.Action.End
import Mathlib.Order.Preorder.Chain
/-!
# Action on flags
Order is... |
Opposite.lean | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Opposites
/-!
# Results about `IsRegular` and `MulOpposite`
-/
variable {R} [Mul R]
open MulOpposite
@[to_additive (attr := simp)]
theorem isLeftR... |
orderedzmod.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 choice.
From mathcomp Require Import ssrAC div fintyp... |
Triplewise.lean | /-
Copyright (c) 2025 Joseph Myers, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yaël Dillies
-/
import Aesop
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.MkIffOfInductiveProp
/-!
# Triplewise predicates on list.
## Main definitions... |
Ker.lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.Algebra.Group.Subgroup.Map
import Mathlib.Tactic.ApplyFun
/-!
# Kernel and range of group homomorphisms
We define and prove results about the kernel and ra... |
FixedPointFree.lean | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.GroupTheory.Perm.Cycle.Type
/-!
# Fixed-point-free automorphisms
This file defines fixed-point-free automorphisms and proves some basic properties.... |
LeftRightNhds.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.Algebra.Ring.Pointwise.Set
import Mathlib.Order.Filter.AtTopBot.CompleteLattice
import Mathlib.Order.Filter.AtTopBot.G... |
End.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.Ring.Action.Group
import Mathlib.Algebra.Ring.Aut
/-!
# Ring automorphisms
This file defines the automorphism... |
Schnirelmann.lean | /-
Copyright (c) 2023 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta, Doga Can Sertbas
-/
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Data.Nat.ModEq
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.Real.Archimedea... |
Hadamard.lean | /-
Copyright (c) 2023 Xavier Généreux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Généreux
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
import Mathlib.Analysis.Complex.PhragmenLindelof
/-!
# Hadamard three-lines Theorem
In this file we present a ... |
Functoriality.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.RepresentationTheory.Homological.GroupHomology.LowDegree
/-!
# Functoriality of group homology
Given a commutative ring `k`, a group homomorphi... |
Positivity.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler, Michael Stoll
-/
import Mathlib.Analysis.Complex.TaylorSeries
import Mathlib.Analysis.Complex.Positivity
import Mathlib.NumberTheory.ArithmeticFunction
i... |
MappingCone.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
import Mathlib.Algebra.Homology.HomotopyCofiber
/-! # The mapping cone of a morphism of cochain complexes
In this ... |
ssrnotations.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
(******************************************************************************)
(* - Reserved notation for various arithmetic and algebraic operations: ... |
numdomain.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 choice.
From mathcomp Require Import ssrAC div fintyp... |
MeasurableEquiv.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.Group.Arithmetic
/-!
# (Scalar) multiplication and (vector) addition as measurable equivalences
In this file we define the following ... |
CommandStart.lean | /-
Copyright (c) 2025 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Tactic.Linter.Header
/-!
# The `commandStart` linter
The `commandStart` linter emits a warning if
* either a command does not start at the beginning ... |
Terminal.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving terminal object
Constructions to relate the n... |
finfun.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 choice.
From mathcomp Require Import fintype tuple.
... |
all_boot.v | Require Export ssreflect.
Require Export ssrbool.
Require Export ssrfun.
Require Export eqtype.
Require Export ssrnat.
Require Export seq.
Require Export choice.
Require Export monoid.
Require Export nmodule.
Require Export path.
Require Export div.
Require Export fintype.
Require Export fingraph.
Require Export tuple.... |
InteractiveUnfold.lean | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Batteries.Lean.Position
import Mathlib.Tactic.NthRewrite
import Mathlib.Tactic.Widget.SelectPanelUtils
import Mathlib.Lean.GoalsLocation
import Mathlib.Lea... |
Variance.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Kexing Ying
-/
import Mathlib.Probability.Moments.Covariance
/-!
# Variance of random variables
We define the variance of a real-valued random variable as `Var[... |
Rename.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import Mathlib.Algebra.MvPolynomial.Eval
/-!
# Renaming variables of polynomials
This file establishes the `rename` operation on mul... |
ContinuousFunctionalCalculus.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Tactic.Core
import Mathlib.Tactic.FunProp
import Aesop
/-!
# Tactics for the continuous functional calculus
At the moment, these tactics are just wra... |
attribute.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.Algebra.Order.Field.Basic
import Mathlib.Tactic.Bound
/-!
## Tests for the `@bound` attribute
Verify that our heuristic for the priority of a decl... |
ssrint.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 seq.
From mathcomp Require Import fintype finfun b... |
all.v | From mathcomp Require Export all_boot.
From mathcomp Require Export all_order.
From mathcomp Require Export all_fingroup.
From mathcomp Require Export all_algebra.
From mathcomp Require Export all_solvable.
From mathcomp Require Export all_field.
From mathcomp Require Export all_character.
|
EquivFin.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Fintype.Card
import Mathlib.Data.List.NodupEquivFin
/-!
# Equivalences between `Fintype`, `Fin` and `Finite`
This file defines the bijection bet... |
Predicate.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Localization.Construction
/-!
# Predicate for localized categories
In this file, a predicate `L.IsLocalization W` is introduced for a functor `... |
Imo1960Q2.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Real.Sqrt
/-!
# IMO 1960 Q2
For what values of the variable $x$ does the following inequality hold:
\[\dfrac{4x^2}{(1 - \sqrt {2x + 1})^2} < ... |
IsBounded.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.Group.Unbundled.Abs
import Mathlib.Algebra.Ord... |
Limits.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.Algebra.Category.FGModuleCat.Basic
import Mathlib.Algebra.Category.ModuleCat.EpiMono
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.Algebr... |
NatCast.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, Yuyang Zhao
-/
import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
import Mathlib.Algebra.Order.ZeroLEOne
import Mathli... |
Clopen.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.Data.Set.Subset
import Mathlib.Topology.Clopen
import Mathlib.Topology.Connected.Basic
/-!
# Connected subsets and th... |
ZMod.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Data.ZMod.Basic
/-!
# `ZMod p` is a field
-/
namespace ZMod
variable (p : ℕ) [hp : Fact p.Prime]
private theorem mul_... |
Slope.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.Analysis.Calculus.Deriv.Add
import Mathlib.LinearAlgebra.AffineSpace.Slope
import Mathlib.Topology.Algebra.Module.PerfectSpace
/-!
# Derivative as t... |
Hofer.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Hofer's lemma
This is an elementary lemma about complete metric spaces. It is motivated by an
application to the ... |
Order.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos Fernandez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
import Mathlib.Data.ENat.Basic
import Mathlib.Data.Finsupp.Weight
import Mathlib.RingTh... |
closed_field.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 choice ssrnat seq.
From mathcomp Require Import fintype 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 seq div.
From mathcomp Require Import choice fintype prim... |
CharZero.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Notation.Support
import Mathlib.Data.Int.Cast.Field
import Mathlib.Data.Int.Cast.Lemmas
import Mathlib.Data.Int.Cast.Pi
/-!
# Injectivity of `... |
Transfer.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.GroupTheory.Complement
import Mathlib.GroupTheory.Sylow
/-!
# The Transfer Homomorphism
In this file we construct the transfer homomorphism.
## Ma... |
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