filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Notation.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 Mathlib.Data.Finsupp.Single
/-!
# Notation for `Finsupp`
This file provides `fun₀ | 3 => a | 7 => b` notation for `Finsupp`, which desugars to
`Finsupp.update` and... |
Defs.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Group.InjSurj
import Mathlib.Algebra.Group.Units.Defs
import Mathlib.Data.Setoid.Basic
import Mathlib.Tactic.FastInstance
/-!
# Congruen... |
LinearOrder.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Batteries.Classes.Order
import Batteries.Tactic.Trans
import Mathlib.Data.Ordering.Basic
import Mathlib.Tactic.ExtendDoc
import Mathlib.Tactic.Lemma
... |
Defs.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Control.Functor
import Mathlib.Data.SProd
impo... |
Powerset.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Lattice.Union
import Mathlib.Data.Multiset.Powerset
import Mathlib.Data.Set.Pairwise.Lattice
/-!
# The pow... |
SmallHom.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.CategoryTheory.Localization.HomEquiv
import Mathlib.Logic.Small.Defs
/-!
# Shrinking morphisms in localized categories
Given a class of morphisms `W : Morphism... |
Star.lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Algebra.Module.Equiv.Defs
import Mathlib.Algebra.Star.Basic
/-!
# Notation for star-linear maps
This is in a separate file as a it is not needed un... |
oldObtain.lean | /-
Copyright (c) 2024 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
import Mathlib.Tactic.Linter.OldObtain
/-! Tests for the `oldObtain` linter. -/
set_option linter.oldObtain true
-- These cases are fine.
theorem foo : True :=... |
Centering.lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Probability.Martingale.Basic
/-!
# Centering lemma for stochastic processes
Any `ℕ`-indexed stochastic process which is adapted and integrable can be wri... |
Enum.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yakov Pechersky, Eric Wieser
-/
import Mathlib.Data.List.Basic
/-!
# Properties of `List.enum`
## Deprecation note
Many lemmas in this file have been replaced by the... |
LiminfLimsup.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.MeasureTheory.Covering.DensityTheorem
/-!
# Liminf, limsup, and uniformly locally doubling measures.
This file is a place to collect lemmas about liminf an... |
RegularExpressions.lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import Mathlib.Computability.Language
import Mathlib.Tactic.AdaptationNote
/-!
# Regular Expressions
This file contains the formal definition for regular expressions and ... |
Covolume.lean | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Analysis.BoxIntegral.UnitPartition
import Mathlib.LinearAlgebra.FreeModule.Finite.CardQuotient
import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpac... |
Girth.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.Combinatorics.SimpleGraph.Acyclic
import Mathlib.Data.ENat.Lattice
/-!
# Girth of a simple graph
This file defines the girth and the extended girth of a ... |
Generator.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.Category.ModuleCat.Presheaf.Abelian
import Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Free
im... |
Reflexive.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Robin Carlier
-/
import Mathlib.CategoryTheory.Limits.Final
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.KernelPair
/... |
Comma.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Comma.Arrow
import Mathlib.CategoryTheory.Comma.Over.Basic
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
import Mathlib.Categor... |
frobenius.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 div.
From mathcomp Require Import fintype bigop prime finset fingroup morphism.
From mathcom... |
FinitePresentation.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.LinearAlgebra.FreeModule.Finite.Basic
import Mathlib.LinearAlgebra.Isomorphisms
import Mathlib.LinearAlgebra.TensorProduct.RightExactness
import Mathlib.Ring... |
Pseudofunctor.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Calle Sönne
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Oplax
import Mathlib.CategoryTheory.Bicategory.Functor.Lax
import Mathlib.Tactic.CategoryTheory.ToApp
/-!
# P... |
UniformConvergence.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.UniformSpace.Cauchy
/-!
# Uniform convergence
A sequence of functions `Fₙ` (with values in a metric space) converges uniformly on a se... |
CongruenceSubgroups.lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Data.Real.Basic
import Mathlib.LinearAlgebra.Matrix.Integer
import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
/-!
# Congruence subgroups
Th... |
imset2_finset.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Check @imset2_pair.
|
HomologicalFunctor.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.ShortComplex.Exact
import Mathlib.CategoryTheory.Shift.ShiftSequence
import Mathlib.CategoryTheory.Triangulated.Functor
import Mathlib.CategoryT... |
Evaluation.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.Limits.Shapes.Products
import Mathlib.CategoryTheory.Functor.EpiMono
/-!
# Adjunctions involving evaluation
We show that evaluation of functo... |
Imo2008Q2.lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib.Data.Real.Basic
import Mathlib.Data.Set.Finite.Lattice
import Mathlib.Tactic.Abel
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
impo... |
Defs.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.Data.Finset.Preimage
import Mathlib.Data.Finset.Prod
import Mathlib.Order.Hom.WithTopBot
import Mathlib.Order.Interval.Set.UnorderedInterval
/-!
# Locally... |
VertexGroup.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Equiv.Defs
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.PathCategory.Basic
i... |
Finiteness.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.LinearAlgebra.Dimension.Constructions
import Mathlib.LinearAlgebra.Dimension.Finite
/-!
# A module over a d... |
Lattice.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Gabriel Ebner, Yury Kudryashov
-/
import Mathlib.Data.Set.Accumulate
import Mathlib.Order.ConditionallyCompleteLattice.Finset
import Mathlib.Order.Int... |
Presheaf.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Mario Carneiro, Reid Barton, Andrew Yang
-/
import Mathlib.Topology.Category.TopCat.Opens
import Mathlib.CategoryTheory.Adjunction.Unique
import Mathlib.CategoryTheory.Func... |
DiscreteQuotient.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Adam Topaz
-/
import Mathlib.Data.Setoid.Partition
import Mathlib.Topology.LocallyConstant.Basic
import Mathlib.Topology.Separation.Regular
import Mathlib.Topology.Connected.T... |
all_order.v | Require Export order.
|
Isometry.lean | /-
Copyright (c) 2021 François Sunatori. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: François Sunatori
-/
import Mathlib.Analysis.Complex.Circle
import Mathlib.LinearAlgebra.Determinant
import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic
/-!
# Isometries o... |
Average.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Lua Viana Reis, Oliver Butterley
-/
import Mathlib.Dynamics.BirkhoffSum.Basic
import Mathlib.Algebra.Module.Basic
/-!
# Birkhoff average
In this file we define `bir... |
Extension.lean | import Mathlib.RingTheory.Extension.Basic
deprecated_module (since := "2025-05-11")
|
instances.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Order.GroupWithZero.Synonym
import Mathlib.Algebra.Order.Ring.Nat
lemma foo (a b : ℕ) (ha : a ≠ 0) (hb : b ≠ 0) : a * b ≠ 0 := by
apply_rules [m... |
Prod.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.Order.Group.Defs
import Mathlib.Algebra.Order.Monoid.Prod
import Mathlib.Tactic.Linter.Depreca... |
Finite.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.Data.Finite.Sum
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.GroupTheory.Perm.Support
import Mathlib.Logic.Equiv.Fintype
/-!
# Permutations on... |
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... |
Pi.lean | /-
Copyright (c) 2024 Judith Ludwig, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Judith Ludwig, Christian Merten
-/
import Mathlib.LinearAlgebra.TensorProduct.Tower
import Mathlib.LinearAlgebra.Pi
/-!
# Tensor product and products
In this file w... |
Basic.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Jireh Loreaux
-/
import Mathlib.Algebra.Ring.Hom.InjSurj
import Mathlib.Deprecated.RingHom
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module (sinc... |
Basic.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.Probability.Independence.Kernel
import Mathlib.MeasureTheory.Constructions.Pi
import Mathlib.MeasureTheory.Group.Convolution
/-!
# Independence of sets of... |
Imo1994Q1.lean | /-
Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Finset.Sort
import Mathlib.Order.Interval.Finset.F... |
Ker.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, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import Mathlib.Algebra.Group.Subgroup.Ker
import Mathlib.Algebra.Module.Submodule.... |
autolabel.lean | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster, Damiano Testa
-/
import Lean.Elab.Command
/-!
# Automatic labelling of PRs
This file contains the script to automatically assign a GitHub label to a PR.
## Label definit... |
AlgebraInstances.lean | /-
Copyright (c) 2024 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.RingTheory.IntegralClosure.IsIntegralClosure.Basic
import Mathlib.RingTheor... |
Union.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.Finset.Fold
import Mathlib.Data.Multiset.Bind
import Mathlib.Order.SetNotation
/-!
# Unions of finite sets
This file defines the union of a fami... |
BumpFunction.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.Calculus.BumpFunction.FiniteDimension
import Mathlib.Geometry.Manifold.ContMDiff.Atlas
import Mathlib.Geometry.Manifold.ContMDiff.NormedSpac... |
AEMeasurable.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Measure.Trim
import Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated
/-!
# Almost everywhere measurable functions
A funct... |
nilpotent.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 fintype div bigop prime finset fingroup morphism.
Fro... |
Set.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.Data.Set.Notation
import Mathlib.Order.SetNotation
import Mathlib.Logic.Embedding.Basic
import Mathlib.Logic.Pairwise
import Mathlib.Da... |
VerticalComposition.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.CategoryTheory.CatCommSq
import Mathlib.CategoryTheory.GuitartExact.Basic
/-!
# Vertical composition of Guitart exact squares
In this file, we show that the ve... |
Blocks.lean | /-
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
-/
import Mathlib.Algebra.Pointwise.Stabilizer
import Mathlib.Data.Setoid.Partition
import Mathlib.GroupTheory.GroupAction.Pointwise
import Mathlib.GroupTh... |
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... |
Torsion.lean | /-
Copyright (c) 2022 Julian Berman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Berman
-/
import Mathlib.GroupTheory.PGroup
import Mathlib.LinearAlgebra.Quotient.Defs
/-!
# Torsion groups
This file defines torsion groups, i.e. groups where all elements hav... |
Module.lean | /-
Copyright (c) 2022 Dylan MacKenzie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dylan MacKenzie
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.Module.Defs
import Mathlib.Tactic.Abel
/-!
# Summation by parts
-/
namespace Finset
variable ... |
center.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 bigop finset fingroup morphism perm.
From math... |
Center.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.Basic
import Mathlib.GroupTheory.Submonoid.Center
/-!
# Centers of subgroups
-/
assert_not_exists MonoidWithZero Multiset
variable... |
PrimeMultiplicity.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes
-/
import Mathlib.RingTheory.Multiplicity
import Mathlib.RingTheory.Valuation.Basic
/-!
# `multiplicity` of a prime in an integral domain as an additive... |
Antisymmetrization.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.Logic.Relation
import Mathlib.Order.Hom.Basic
import Mathlib.Tactic.Tauto
/-!
# Turning a preorder into a partial order
This file allows to make a preord... |
Order.lean | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Topology.Algebra.IsUniformGroup.Defs
import Mathlib.Topology.Order.Basic
import Mathlib.Topology.UniformSpace.UniformConvergence
/-!
# TendstoUniforml... |
Embedding.lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import Mathlib.Data.Fin.Basic
import Mathlib.Logic.Embedding.Basic
/-!
# Embeddings of `Fin n`
`Fin n` is the type whose elements are natural numbers... |
rat.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 prime fintype fi... |
DoublingConst.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Combinatorics.Additive.PluenneckeRuzsa
import Mathlib.Data.Finset.Density
/-!
# Doubling and difference constants
This file defines the doubling and diff... |
Trigonometric.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.Data.Complex.Exponential
/-!
# Trigonometric and hyperbolic trigonometric functions
This file contains the definitions of the s... |
MatrixExponential.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Analysis.Normed.Algebra.Exponential
import Mathlib.Analysis.Matrix
import Mathlib.LinearAlgebra.Matrix.ZPow
import Mathlib.LinearAlgebra.Matrix.Hermitian
imp... |
Relation.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.WSeq.Basic
import Mathlib.Logic.Relation
/-!
# Relations between and equivalence of weak sequences
This file defines a relation between w... |
Bivariate.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.RingTheory.AdjoinRoot
/-!
# Bivariate polynomials
This file introduces the notation `R[X][Y]` for the polynomial ring `R[X][X]` in two variables,
and the notat... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
Pow.lean | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Convex.SpecificFunctions.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
/-!
# Convexity properties of `rpow`
We prove basic co... |
Card.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, Huỳnh Trần Khanh, Stuart Presnell
-/
import Mathlib.Data.Finset.Sym
import Mathlib.Data.Fintype.Sum
import Mathlib.Data.Fintype.Prod
import Math... |
all_ssreflect.v | Attributes deprecated(since="mathcomp 2.5.0",
note="Use 'all_boot' and/or 'all_order' instead.").
From mathcomp Require Export all_boot.
From mathcomp Require Export preorder.
From mathcomp Require Export order.
|
Matrix.lean | /-
Copyright (c) 2025 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yunzhou Xie, Jujian Zhang
-/
import Mathlib.Algebra.Azumaya.Defs
import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
/-!
# Matrix algebra is an Azumaya algebra over R
In this file we p... |
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... |
IdempotentFG.lean | /-
Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import Mathlib.Algebra.Ring.Idempotent
import Mathlib.Order.Basic
import Mathlib.RingTheory.Finiteness.Nakayama
/-!
## Lemmas on idempo... |
ProjectiveSpecialLinearGroup.lean | /-
Copyright (c) 2023 Wen Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wen Yang
-/
import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
/-!
# Projective Special Linear Group
## Notation
In the `MatrixGroups` locale:
* `PSL(n, R)` is a shorthand for `Matri... |
Coherence.lean | import Mathlib.Tactic.CategoryTheory.Coherence
open CategoryTheory
universe w v u
section Monoidal
variable {C : Type u} [Category.{v} C] [MonoidalCategory C]
open scoped MonoidalCategory
-- Internal tactics
example (X₁ X₂ : C) :
((λ_ (𝟙_ C)).inv ⊗ₘ 𝟙 (X₁ ⊗ X₂)) ≫ (α_ (𝟙_ C) (𝟙_ C) (X₁ ⊗ X₂)).hom ≫
(... |
Contraction.lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Antoine Labelle
-/
import Mathlib.LinearAlgebra.Dual.Lemmas
import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# Contractions
Given modules $M, N$ over a commutative ring $R$, t... |
Real.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot, Eric Wieser, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.LinearAlgebra.Basis.VectorSpace
/-!
# Basic facts about real ... |
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... |
Configuration.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Combinatorics.Hall.Basic
import Mathlib.Data.Matrix.Rank
import Mathlib.LinearAlgebra.Projectivization.Constructions
/-!
# Configurations of Points ... |
Basic.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Order.PropInstances
import Mathlib.Tactic.ByContra
import Mathlib.Tactic.Lift
import Mathlib.Tactic.Tauto
import Mathlib.Util.Delabora... |
SmoothApprox.lean | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.BumpFunction.Convolution
import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
/-!
# Density of smooth functions in the sp... |
Similarity.lean | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid, Newell Jensen
-/
import Mathlib.Topology.MetricSpace.Congruence
/-!
# Similarities
This file defines `Similar`, i.e., the equivalence between indexed sets of poin... |
NhdsSet.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Order.Basic
/-!
# Set neighborhoods of intervals
In this file we prove basic theorems about `𝓝ˢ s`,
where `s` is one of the intervals
`Se... |
CoherentSheaves.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Canonical
import Mathlib.CategoryTheory.Sites.Coherent.Basic
import Mathlib.CategoryTheory.Sites.EffectiveEpimorphic
/-!
# Sheaves for th... |
Basic.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jon Eugster
-/
import Mathlib.Lean.Meta
/-!
# Additions to `Lean.Elab.Tactic.Basic`
-/
open Lean Elab Tactic
namespace Lean.Elab.Tactic
/-- Return expected type ... |
Finset.lean | /-
Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
import Mathlib.Algebra.Order.Group.OrderIso
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Algebra.Order.Monoid.Unbundled.Min... |
RestrictScalars.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.Module.Presentation.DirectSum
import Mathlib.Algebra.Module.Presentation.Cokernel
/-!
# Presentation of the restriction of scalars of a module
Given a ... |
AddChar.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Algebra.BigOperators.Pi
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Group.Subgroup.Ker
import Mathlib.Algebra.Group.TransferIn... |
DocPrime.lean | import Mathlib.Tactic.Linter.DocPrime
import Mathlib.Tactic.Lemma
set_option linter.docPrime true
-- no warning on a primed-declaration with a doc-string containing `'`
/-- X' has a doc-string -/
def X' := 0
-- no warning on a declaration whose name contains a `'` *and does not end with it*
def X'X := 0
-- A list o... |
Ext.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Adam Topaz
-/
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algebra.Homology.Opposite
import Mathlib.CategoryTheory.Abelian.LeftDerived
import Mathlib.Ca... |
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... |
Bracket.lean | /-
Copyright (c) 2021 Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Lutz, Oliver Nash
-/
import Mathlib.Tactic.TypeStar
/-!
# Bracket Notation
This file provides notation which can be used for the Lie bracket, for the commutator of two
subgroups... |
WhatsNew.lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Mathlib.Init
/-!
Defines a command wrapper that prints the changes the command makes to the
environment.
```
whatsnew in
theorem foo : 42 = 6 * 7 := rf... |
Nilpotent.lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Ines Wright, Joachim Breitner
-/
import Mathlib.GroupTheory.Solvable
import Mathlib.GroupTheory.Sylow
import Mathlib.Algebra.Group.Subgroup.Order
import Mathlib.GroupTheo... |
AlgebraicClosure.lean | import Mathlib.Algebra.Algebra.Rat
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
variable {k : Type*} [Field k]
example : (AddCommMonoid.toNatModule : Module ℕ (AlgebraicClosure k)) =
@Algebra.toModule _ _ _ _ (AlgebraicClosure.instAlgebra k) := by
with_reducible_and_instances rfl
example : (AddCom... |
choice.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.
(**************************************************... |
monoid.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun.
(******************************************************************************)
(* Group-like structures ... |
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