filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
BinaryProducts.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Preserve... |
Basic.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Endomorphism
/-!
# The center of a category
Given a category `C`, we introduce an abbreviation `CatCenter C` for
the center of the category `C`,... |
Smooth.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.RingTheory.RingHom.FinitePresentation
import Mathlib.RingTheory.Smooth.Locus
/-!
# Smooth ring homomorphisms
In this file we define smooth ring homomorphis... |
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... |
Limits.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.Category.ModuleCat.Basic
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.Algebra.Colimit.Module
import Mathlib.Algebra.Module.Shrink
/-!... |
Symmetric.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Subspace
import Mathlib.Analysis.Normed.Operator.Banach
import Mathlib.LinearAlgebra.Sesqui... |
Expr.lean | import Mathlib.Lean.Expr.ReplaceRec
import Mathlib.Data.Nat.Notation
import Lean.Elab.Command
open Lean Meta Elab Command
section replaceRec
/-! Test the implementation of `Expr.replaceRec` -/
/-- Reorder the last two arguments of every function in the expression.
(The resulting term will generally not be a type-c... |
fraction.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 div seq.
From mathcomp Require Import ssrAC choice tuple ... |
ZMod.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Data.ZMod.Basic
/-!
# The `ZMod n`-algebra structure on rings whose characteristic divides `n`
-/
assert_not_exis... |
Compactum.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Monad.Types
import Mathlib.CategoryTheory.Monad.Limits
import Mathlib.CategoryTheory.Equivalence
import Mathlib.Topology.Category.CompHaus.Basic... |
StoneSeparation.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.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Join
/-!
# Stone's separation theorem
This file proves Stone's separation theorem. This tells ... |
Bochner.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.MeasureTheory.Integral.Bochner.Basic
import Mathlib.MeasureTheory.Integral.Bochner.L1
import Mathlib.Me... |
Basic.lean | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Data.Nat.Bitwise
import Mathlib.SetTheory.Ordinal.Family
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module
"Th... |
Examples.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.CategoryTheory.Galois.Basic
import Mathlib.CategoryTheory.Action.Concrete
import Mathlib.CategoryTheory.Action.Limits
/-!
# Examples of Galois cat... |
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... |
ParallelPair.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Final
/-!
# Conditions for `parallelPair` to be initial
In this file we give sufficient conditions on a category... |
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... |
Regular.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.Cardinal.Cofinality
import Mathlib.SetTheory.Ordinal.FixedPoint
/-!
# Regular cardinals
This ... |
OptionalSampling.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Order.SuccPred.LinearLocallyFinite
import Mathlib.Probability.Martingale.Basic
/-!
# Optional sampling theorem
If `τ` is a bounded stopping time and `σ` ... |
Parity.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.Algebra.Group.Even
/-!
# The cardinality of `Fin 2` is even.
-/
variable {α : Type*}
namespace Fintype
instance I... |
cc.lean | example (a₁ a₂ b₁ b₂ c d : Nat) :
a₁ = c → a₂ = c →
b₁ = d → d = b₂ →
a₁ + b₁ + a₁ = a₂ + b₂ + c := by
grind
example (a b c : Prop) : (a ↔ b) → ((a ∧ (c ∨ b)) ↔ (b ∧ (c ∨ a))) := by
grind
example (a b c d : Prop)
[d₁ : Decidable a] [d₂ : Decidable b] [d₃ : Decidable c] [d₄ : Decidable ... |
Incenter.lean | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Geometry.Euclidean.Altitude
import Mathlib.Geometry.Euclidean.SignedDist
import Mathlib.Geometry.Euclidean.Sphere.Tangent
import Mathlib.Tactic.Positivity.... |
Group.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Order.Group.Basic
import Mathlib.Topology.Algebra.Group.Defs
import Mathlib.Topology.Order.LeftRightNhds
/-!
# Topology on a linear ordered ... |
Basic.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.Monoid.Unbundled.Basic
import Mathlib.Algebra.Order.Sub.Defs
import Mathlib.Util.AssertE... |
SumTransform.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.Computability.AkraBazzi.GrowsPolynomially
import Mathlib.Analysis.Calculus.Deriv.Inv
import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
import ... |
Compact.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.RingTheory.DedekindDomain.Factorization
import Mathlib.RingTheory.DiscreteValuationRing.Basic
import Mathlib.RingTheory.HopkinsLevitzki
import Mathlib.RingTh... |
Cocartesian.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.CategoryTheory.FiberedCategory.HomLift
/-!
# Cocartesian morphisms
This file defines cocartesian resp. strongly cocartesian morphisms with respect to a fu... |
Basic.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Nailin Guan, Yuyang Zhao
-/
import Mathlib.Algebra.Category.Grp.FiniteGrp
import Mathlib.Topology.Algebra.Group.ClosedSubgroup
import Mathlib.Topology.Algebra.ContinuousMon... |
MorphismProperty.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten, Joël Riou, Adam Topaz
-/
import Mathlib.AlgebraicGeometry.Pullbacks
import Mathlib.CategoryTheory.Sites.MorphismProperty
/-!
# Site defined by a morphism property... |
LongNames.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Lean.Name
import Mathlib.Lean.Expr.Basic
import Lean.Elab.Command
/-!
# Commands `#long_names` and `#long_instances`
For finding declarations with excess... |
coe.lean | import Mathlib.Tactic.Coe
example : { n : Nat // n > 3 } → Nat := (↑)
|
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 Batteries.Tactic.Init
import Mathlib.Logic.Function.Defs
/-!
# Binary map of options
This file defines the binary map of `Option`. This is mostly useful to defin... |
RewriteSearch.lean | /-
Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Lean.Meta.Tactic.Rewrites
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.List.EditDistance.Estimator
import Mathlib.Data.MLList.BestFirst
import Mathl... |
Multiplicity.lean | /-
Copyright (c) 2022 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen, Mantas Bakšys
-/
import Mathlib.Algebra.Order.Ring.Basic
import Mathlib.Algebra.Ring.GeomSum
import Mathlib.Algebra.Ring.Int.Parity
import Mathlib.Data.Nat.Choose.Sum
import Math... |
Basic.lean | /-
Copyright (c) 2023 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Yaël Dillies, Jineon Baek
-/
import Mathlib.Algebra.EuclideanDomain.Int
import Mathlib.Algebra.GCDMonoid.Finset
import Mathlib.Algebra.GCDMonoid.Nat
import Mathlib.Algebr... |
Cylinder.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.ModelCategory.Basic
import Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant
/-!
# Cylinders
We introduce a notion of cylinder for an objec... |
FixedPointApproximants.lean | /-
Copyright (c) 2024 Ira Fesefeldt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ira Fesefeldt
-/
import Mathlib.SetTheory.Ordinal.Arithmetic
/-!
# Ordinal Approximants for the Fixed points on complete lattices
This file sets up the ordinal-indexed approximation t... |
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... |
Set.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Data.Set.FunctorToTypes
import Mathlib.CategoryTheory.Limits.Lattice
import Mathlib.CategoryTheory.Limits.Preserves.Basic
import Mathlib.CategoryTheory.Limits.Ty... |
FiniteDimensional.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Projection.Basic
import Mathlib.Analysis.InnerProductSpace.Projection.Reflection
import Math... |
OfFn.lean | /-
Copyright (c) 2025 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Polynomial.Degree.Lemmas
import Mathlib.Data.List.ToFinsupp
import Mathlib.LinearAlgebra.Pi
/-!
#... |
Invertible.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.Group.Invertible.Basic
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Theorems about invertible elements in a `GroupWithZero`
We intentiona... |
Limits.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Isomorphisms about functors which preserve (co)limits
If `G` preserves limits, and `C` and `D` ... |
Functors.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Limits.Preserves.Ulift
import Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves
import Mathlib.CategoryTheory.Sites.Whiskering
i... |
Units.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.Semiconj.Units
/-!
# Lemmas about commuting pairs of elements involving uni... |
DualNumber.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.Algebra.DualNumber
import Mathlib.Data.Matrix.Basic
/-!
# Matrices of dual numbers are isomorphic to dual numbers over matrices
Showing this for the more g... |
Bicones.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Cones
import Mathlib.CategoryTheory.FinCategory.Basic
/-!
# Bicones
Given a category `J`, a walking `Bicone J` is a category whose ob... |
Basis.lean | /-
Copyright (c) 2025 Raphael Douglas Giles. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Raphael Douglas Giles, Zhixuan Dai, Zhenyan Fu, Yiming Fu, Jingting Wang, Eric Wieser
-/
import Mathlib.LinearAlgebra.SymmetricAlgebra.Basic
import Mathlib.LinearAlgebra.Dimensi... |
QuasiMeasurePreserving.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.MeasureTheory.Measure.AbsolutelyContinuous
import Mathlib.MeasureTheory.OuterMeasure.BorelCantelli
/-!
# Quasi Measure Preserving Func... |
Coyoneda.lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Types.Basic
import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
/-!
# `(𝟙_ C ⟶ -)` is a lax monoidal f... |
Basic.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 Mathlib.ModelTheory.Syntax
import Mathlib.ModelTheory.Semantics
import Mathlib.ModelTheory.Algebra.Ring.Basic
import Mathlib.Algebra.Field.MinimalAxioms
import Ma... |
Induction.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Algebra.Category.ModuleCat.Free
import Mathlib.Topology.Category.Profinite.Nobeling.Span
import Mathlib.Topology.Category.Profinite.Nobeling.Succes... |
Gluing.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.Gluing
import Mathlib.Geometry.RingedSpace.OpenImmersion
import Mathlib.Geometry.RingedSpace.LocallyRingedSpace.HasColimits
/-!
# Gluing Structured... |
gfunctor.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 fintype.
From mathcomp Require Import bigop finset fingroup morphism automorphism.
From math... |
Field.lean | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Algebra.CharP.Two
import Mathlib.SetTheory.Nimber.Basic
import Mathlib.Tactic.Abel
import Mathlib.Tactic.Linter.DeprecatedModul... |
ExpLog.lean | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Normed.Algebra.Spectrum
import Mathlib.Analysis.SpecialFunctions.Exponential
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalcu... |
ToLin.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import Mathlib.Algebra.Algebra.Subalgebra.Tower
import Mathlib.Data.Finite.Sum
import Mathlib.Data.Matrix.Block
import Mathl... |
PossibleTypes.lean | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.GroupTheory.Perm.Cycle.Concrete
/-! # Possible cycle types of permutations
* For `m : Multiset ℕ`, `Equiv.Perm.exists_with_cycleType_i... |
SchurZassenhaus.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.GroupTheory.Transfer
/-!
# The Schur-Zassenhaus Theorem
In this file we prove the Schur-Zassenhaus theorem.
## Main results
- `Subgroup.exists_ri... |
Indization.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.Limits.Indization.Category
import Mathlib.CategoryTheory.Preadditive.Transfer
import Mathlib.CategoryTheory.Preadditive.Opposite
import Ma... |
Zip.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import Mathlib.Data.List.Forall2
/-!
# zip & unzip
This file provides results about `List.zipWith`, `List.zip` and `List.unzip` (definitions are in
core ... |
GameMultiplication.lean | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.SetTheory.Game.Basic
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module
"This m... |
Basic.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.Action.Basic
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.Group.Pointwise.Set.Scal... |
Defs.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.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.ContDiff.Defs
/-!
# One-dimensional iterated derivatives
We define the `n`-th de... |
Hensel.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
-/
import Mathlib.Algebra.Polynomial.Identities
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.NumberTheory.Padics.PadicIntegers
import Mathlib.Topology.A... |
HNNExtension.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 Mathlib.Algebra.Ring.CharZero
import Mathlib.Algebra.Ring.Int.Units
import Mathlib.GroupTheory.Coprod.Basic
import Mathlib.GroupTheory.Complement
/-!
## HNN Exte... |
Counit.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.MvPolynomial.Eval
/-!
## Counit morphisms for multivariate polynomials
One may consider the ring of multivariate polynomials `MvPolynomial A ... |
Dart.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Combinatorics.SimpleGraph.Basic
import Mathlib.Data.Fintype.Sigma
/-!
# Darts in graphs
A `Dart` or half-edge or bond in a graph is an ordered pair of adja... |
Centralizer.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Center
import Mathlib.Algebra.Group.Subsemigroup.Basic
import Mathlib.GroupTheory.Subsemigroup.Center
/-!
# Centralizer... |
SMulAntidiagonal.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.Order.AddTorsor
import Mathlib.Order.WellFoundedSet
/-!
# Antidiagonal for scalar multiplication
Given partially ordered sets `G` and `P`, wi... |
Forall2.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Data.List.Basic
/-!
# Double universal quantification on a list
This file provides an API for `List.Forall₂` (definition in `Data.Lis... |
Lemmas.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
-/
import Mathlib.LinearAlgebra.Basis.Basic
import Mathlib.LinearAlgebra.Dimension.ErdosKaplansky
import Mathlib.LinearAlgebra.Dual.Basis
im... |
Spec.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Justus Springer
-/
import Mathlib.Geometry.RingedSpace.LocallyRingedSpace
import Mathlib.AlgebraicGeometry.StructureSheaf
import Mathlib.RingTheory.Localization.Localizatio... |
Adjunction.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Functor.Derived.LeftDerived
import Mathlib.CategoryTheory.Functor.Derived.RightDerived
/-!
# Derived adjunction
Assume that functors `G : C₁ ⥤ C... |
separable.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 tupl... |
imset2_finset.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Check @imset2_pair.
|
CPolynomial.lean | /-
Copyright (c) 2023 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
import Mathlib.Analysis.Analytic.Constructions
import Mathlib.Analysis.Analytic.CPolynomialDef
/-! # Properties of continuously polynomial functions
We expand the API a... |
Monotone.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.Data.Set.Monotone
import Mathlib.Order.Interval.Set.Disjoint
import Mathlib.Order.SuccPred.Archimedean
/-!
# Monotonicity on intervals
In this file... |
CheckCompositions.lean | import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.Tactic.Recall
universe v₁ v₂ v₃ v u₁ u₂ u₃ u
open CategoryTheory Limits
variable {J : Type u} [Category.{v} J] {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
{E : Type u₃} [Category.{v₃} E] (F : J ⥤ C) (G : C ⥤ D) (H : D ⥤ E)
... |
ConvergenceInMeasure.lean | /-
Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
import Mathlib.MeasureTheory.Function.Egorov
import Mathlib.MeasureTheory.Function.LpSpace.Complete
/-!
# Convergence in measure
We define con... |
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.
... |
Invertible.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Ahmad Alkhalawi
-/
import Mathlib.Data.Matrix.ConjTranspose
import Mathlib.Tactic.Abel
/-! # Extra lemmas about invertible matrices
A few of the `Invertible` lemmas general... |
vector.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 bigop fi... |
Module.lean | import Mathlib.Algebra.Algebra.Rat
import Mathlib.Data.Complex.Module
-- Test that the `SMul ℚ ℂ` instance is correct.
example : (Complex.SMul.instSMulRealComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ ℂ) := by
with_reducible_and_instances rfl
|
mxrepresentation.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... |
Spectrum.lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Analysis.InnerProductSpace.Spectrum
import Mathlib.Data.Matrix.Rank
import Mathlib.LinearAlgebra.Matrix.Diagonal
import Mathlib.LinearAlgebra.M... |
UpstreamableDecl.lean | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Anne Baanen
-/
import ImportGraph.Imports
import Mathlib.Init
/-! # The `upstreamableDecl` linter
The `upstreamableDecl` linter detects declarations that could be moved... |
Congruence.lean | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid, Chu Zheng
-/
import Mathlib.Topology.MetricSpace.Congruence
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.Normed.Group.AddTorsor
import M... |
Irreducible.lean | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.RootSystem.RootPositive
import Mathlib.LinearAlgebra.RootSystem.WeylGroup
import Mathlib.RepresentationTheory.Submodule
/-!
# Irreducible root... |
Limits.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
import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.... |
jordanholder.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 big... |
NatAbs.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Jeremy Tan
-/
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Algebra.Ring.Int.Defs
/-!
# Lemmas about `Int.natAbs`
This fi... |
ExistsAndEq.lean | /-
Copyright (c) 2025 Vasilii Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasilii Nesterov
-/
import Mathlib.Init
/-!
# simproc for `∃ a', ... ∧ a' = a ∧ ...`
This module implements the `existsAndEq` simproc that triggers on goals of the form `∃ a, body`... |
Basic.lean | /-
Copyright (c) 2024 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, Xavier Généreux
-/
import Mathlib.LinearAlgebra.FreeModule.Basic
/-!
# Skew Monoid Algebras
Given a monoid `G` acting on a ring `k`, t... |
WithZeroMulInt.lean | /-
Copyright (c) 2025 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
import Mathlib.GroupTheory.ArchimedeanDensely
import Mathlib.Topology.Algebra.Valued.ValuationTopology
/-!
# Topological results for integer-valued rings
This... |
Pointwise.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Ring.Action.End
import Mathlib.RingTheory.Ideal.Maps
/-! # Pointwise instances on `Ideal`s
This file provides the action `Ideal.pointwiseMulAction`... |
SeparationQuotient.lean | /-
Copyright (c) 2024 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.Topology.Algebra.SeparationQuotient.Hom
/-!
# Lifts of maps to separation quotients of seminormed groups
For any... |
DeleteEdges.lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark, Kyle Miller, Alena Gusakov, Hunter Monroe
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Combinatorics.SimpleGraph.Finite
imp... |
BigOperators.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Group.Finsupp
import Mathlib.Data.Finset.Pairwise
/-!
# Sums of collections of Finsu... |
jacobiSym.lean | import Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol
import Mathlib.Tactic.NormNum.Prime
-- TODO(kmill): remove once the mathlib ToExpr Int instance is removed
set_option eval.pp false
section Csimp
/-!
We test that `@[csimp]` replaces `jacobiSym` (i.e. `J(· | ·)`) and `legendreSym` with
`jacobiSym.fastJacobiSym`... |
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