filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Prod.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.RingTheory.Ideal.Maps
/-!
# Ideals in product rings
For commutative rings `R` and `S` and ideals `I ≤ R`, `J ≤ S`, we define `Ideal.prod I J` as the
pr... |
cyclic.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 bigo... |
Disjointed.lean | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Algebra.Order.PartialSups
import Mathlib.Data.Nat.SuccPred
import Mathlib.Order.Disjointed
/-!
# `Disjointed` for functions on a `SuccAddOrder`
This ... |
DifferentialRing.lean | /-
Copyright (c) 2024 Daniel Weber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Weber
-/
import Mathlib.RingTheory.Derivation.Basic
/-!
# Differential and Algebras
This file defines derivations from a commutative ring to itself as a typeclass, which lets us... |
FractionRing.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import Mathlib.Algebra.Ring.Hom.InjSurj
import Mathlib.Algebra.Field.Equiv
import Mathlib.Algebra.Field.Subfield... |
Partition.lean | /-
Copyright (c) 2021 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Kyle Miller
-/
import Mathlib.Combinatorics.SimpleGraph.Coloring
/-!
# Graph partitions
This module provides an interface for dealing with partitions on simple graphs... |
Closure.lean | /-
Copyright (c) 2023 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.RingTheory.SimpleRing.Basic
import Mathlib.FieldTheory.Normal.Basic
import Mathlib.Order.Closure
import Mathlib.LinearAlgebra.FreeModule.Finite.Matr... |
ExtractGoal.lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Kyle Miller, Damiano Testa
-/
import Lean.Elab.Term
import Lean.Elab.Tactic.ElabTerm
import Lean.Meta.Tactic.Cleanup
import Lean.PrettyPrinter
import Batteries.Lean.Meta.Inac... |
Defs.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.Order.Atoms
import Mathlib.LinearAlgebra.Span.Defs
import Mathlib.LinearAlgebra.AffineSpace.Defs
/-!
# Affine spaces
This file defines affine subspaces (... |
Qify.lean | import Mathlib.Algebra.Order.Field.Rat
import Mathlib.Data.Int.CharZero
import Mathlib.Tactic.Qify
example (a b : ℕ) : (a : ℚ) ≤ b ↔ a ≤ b := by qify
example (a b : ℕ) : (a : ℚ) < b ↔ a < b := by qify
example (a b : ℕ) : (a : ℚ) = b ↔ a = b := by qify
example (a b : ℕ) : (a : ℚ) ≠ b ↔ a ≠ b := by qify
example (a b : ... |
ForgetCorepresentable.lean | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Nat.Hom
import Mathlib.CategoryTheory.Yoneda
/-!
# The... |
Dirichlet.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.NumberTheory.DirichletCharacter.Bounds
import Mathlib.NumberTheory.LSeries.Convolution
import Mathlib.NumberTheory.LSeries.Deriv
import Mathlib.NumberThe... |
Kaehler.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.RingTheory.Extension.Cotangent.Basic
import Mathlib.RingTheory.Smooth.Basic
import Mathlib.Algebra.Module.Projective
import Mathlib.Tactic.StacksAttribute
/... |
Addition.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Group.Support
import Mathlib.Algebra.Module.Basic... |
Strict.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Christian Merten
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
import Mathlib.CategoryTheory.CommSq
/-!
# Pseudofunctors from strict bicategory
This file pr... |
Quotient.lean | /-
Copyright (c) 2022 Alex Kontorovich and Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.MeasureTheory.Constructions.Polish.Basic
import Mathlib.MeasureTheory.Gr... |
Matrix.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Yunzhou Xie
-/
import Mathlib.Algebra.Central.Basic
import Mathlib.Data.Matrix.Basis
/-!
# The matrix algebra is a central algebra
-/
namespace Algebra.IsCentral
variabl... |
Degree.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.Algebra.Polynomial.Degree.Support
import Mathlib.Algebra... |
PartitionOfUnity.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.Geometry.Manifold.Algebra.Structures
import Mathlib.Geometry.Manifold.BumpFunction
import Mathlib.Topology.MetricSpace.PartitionOfUnity
import Mathli... |
Quotient.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yongle Hu
-/
import Mathlib.Algebra.Group.Subgroup.Actions
import Mathlib.RingTheory.FiniteType
import Mathlib.RingTheory.Ideal.Pointwise
import Mathlib.RingTheory.Ideal.Over... |
ssrfun.v | From mathcomp Require Import ssreflect.
From Corelib Require Export ssrfun.
From mathcomp Require Export ssrnotations.
#[export] Set Warnings "-overwriting-delimiting-key".
(* remove above line when requiring Rocq >= 9.0 *)
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
(***********... |
GeneralLinearGroup.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Module.Equiv.Basic
/-!
# The general linear group of linear maps
The general linear group is defined to be the group of invertible linear map... |
Layercake.lean | /-
Copyright (c) 2022 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
/-!
# The layer cake formula / Cavalieri's principle / tail probability formula
In this file we prove the f... |
Defs.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Batteries.Data.Nat.Gcd
import Mathlib.Algebra.Group.Nat.Units
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.... |
Tower.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.RingTheory.Adjoin.FG
/-!
# Adjoining elements and being finitely generated in an algebra tower
## Main results
* `Algebra.fg_trans'`: if `S` is finitely gener... |
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, Mario Carneiro, Yaël Dillies
-/
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Int.Order.Basic
import Mathlib.Logic.Function.Iterate
import Mathlib.Order.Compare
impor... |
Scheme.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.AlgebraicGeometry.Spec
import Mathlib.Algebra.Category.Ring.Constructions
import Mathlib.CategoryTheory.Elementwise
/-!
# The category of schemes
A schem... |
Exterior.lean | import Mathlib.Topology.Compactness.NhdsKer
deprecated_module (since := "2025-07-09")
|
vcharacter.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... |
Tower.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.RingTheory.Noetherian.Basic
/-!
# Finiteness of `IsScalarTower`
We prove that given `IsScalarTower F K A`, if `A` is finite as a module over `F` then
`A` is fi... |
Lemmas.lean | /-
Copyright (c) 2023 Yael Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yael Dillies
-/
import Batteries.Tactic.Init
import Mathlib.Tactic.ToAdditive
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.TypeStar
import Mathlib.Util.AssertExists
/-! # Lemmas ab... |
Operations.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.Algebra.Order.Group.Indicator
import Mathlib.MeasureTheory.OuterMeasure.Basic
/-!
# Operations on outer measures
In this file we defi... |
SubboxInduction.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.BoxIntegral.Box.Basic
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Induction on subboxes
In this file we prove the following inducti... |
Basic.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.Limits.Preorder
/-!
# Limits and colimits indexed by preorders
In this file, we obtain the following very basic results
about limits and colimit... |
Defs.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison, Adam Topaz
-/
import Mathlib.CategoryTheory.Opposites
import Mathlib.Order.Fin.Basic
import Mathlib.Util.Superscript
/-! # The simplex category
We constru... |
Basic.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.RingTheory.FiniteType
import Mathlib.RingTheory.IntegralClosure.Algebra.Basic
import Mathlib.RingTheory.IntegralClosure.I... |
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.Data.Rat.Encodable
import Mathlib.Topology.MetricSpace.Isometry
import Mathlib.Topology.MetricSpace.ProperSpace
import Mathlib.Topology... |
Datatypes.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, Miyahara Kō
-/
import Batteries.Classes.Order
import Mathlib.Lean.Meta.Basic
import Mathlib.Lean.Meta.CongrTheorems
import Mathlib.Data.Ordering.Basic
/-!
# ... |
Category.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.Constructions.Filtered
import Mathlib.CategoryTheory.Limits.FullSubcategory
import Mathlib.CategoryTheory.Limits.ExactFunctor
impor... |
LocallySurjective.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.Sites.Coherent.ExtensiveTopology
import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison
import Mathlib.CategoryTheory.Sites.Lo... |
Killing.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.InvariantForm
import Mathlib.Algebra.Lie.Semisimple.Basic
import Mathlib.Algebra.Lie.TraceForm
/-!
# Lie algebras with non-degenerate Killing fo... |
Polynomial.lean | import Mathlib.Algebra.Polynomial.Eval.Degree
import Mathlib.Algebra.Polynomial.Inductions
import Mathlib.Tactic.RewriteSearch
set_option autoImplicit true
open Polynomial
-- Fails, but used to work prior to `rw?` moving to `lean4`.
-- -- info: Try this: rw [@natDegree_sub, @sub_eq_neg_add, @natDegree_add_C, @natDeg... |
Basic.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.EuclideanDomain.Defs
import Mathlib.Algebra.Ring.Divisibility.Basic
import Mathlib.Algebra.Ring.Regular
import Mathlib.Algebra.Grou... |
intdiv.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
Projective.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
import Mathlib.MeasureTheory.Constructions.Cylinders
import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
/-!
# Projective measure families a... |
CostructuredArrow.lean | /-
Copyright (c) 2024 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Filtered.OfColimitCommutesFiniteLimit
import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
import Mathlib.CategoryTheory.Li... |
Upto.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Algebra.Order.Sub.Basic
/-!
# `Nat.Upto`
`Nat.Upto p`, with `p` a predicate on `ℕ`, is a subtype of elements `n : ℕ`... |
Defs.lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.Ring.Defs
/-!
# Modules over a ring
In th... |
MeanInequalitiesPow.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.Analysis.Convex.Jensen
import Mathlib.Analysis.Convex.Mul
import Mathlib.Analysis.Convex.SpecificFunctions.Basic
imp... |
spectral.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp.
From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector.
From mathcomp Require Import mxpoly mxred sesqui... |
Imo2015Q6.lean | /-
Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.Order.Group.Int.Sum
import Mathlib.Algebra.Order.Ring.Int
/-!
# IMO 2015 Q6
The sequence $a_1, a_2, \do... |
ConvexBody.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.MeasureTheory.Group.GeometryOfNumbers
import Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls
import Mathlib.NumberTheory.NumberField.CanonicalEmbedd... |
Factorization.lean | /-
Copyright (c) 2022 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey, Patrick Stevens, Thomas Browning
-/
import Mathlib.Algebra.Order.Ring.GeomSum
import Mathlib.Data.Nat.Choose.Central
import Mathlib.Data.Nat.Digits.Lemmas
import Mathlib.... |
imset2_gproduct.v | From mathcomp Require Import all_boot all_fingroup.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Import GroupScope.
Open Scope group_scope.
Check @ker_sdprodm.
|
Lattice.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
-/
import Mathlib.Algebra.Group.Subgroup.Lattice
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra... |
LongFile.lean | import Mathlib.Tactic.Linter.Style
/-
# Testing the `longFile` linter
Things to note:
* `set_option linter.style.longFile 0` disables the linter, allowing us to set a value smaller than
`linter.style.longFileDefValue` without triggering the warning for setting a small value
for the option;
* `guard_msgs ... in #e... |
Inverse.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.Analysis.Analytic.Composition
import Mathlib.Analysis.Analytic.Linear
import Mathlib.Tactic.Positivity
/-!
# Inverse of analytic functions
We ... |
Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yaël Dillies
-/
import Mathlib.Algebra.NoZeroSMulDivisors.Defs
import Mathlib.Algebra.Group.Action.Pi
/-!
# Pi instances for NoZeroSMulDivisors
This file defines instances ... |
PPOptions.lean | /-
Copyright (c) 2024 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Init
/-!
Mathlib-specific pretty printer options.
-/
namespace Mathlib
open Lean
/--
The `pp.mathlib.binderPredicates` option is used to control whether ... |
Trifunctor.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.CategoryTheory.Functor.Category
/-!
# Trifunctors obtained by composition of bifunctors
Given two bifunctors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂` and `G : C₁₂ ⥤ C₃ ⥤ C₄`, we d... |
MStructure.lean | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Algebra.Ring.Idempotent
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Order.Basic
import Mathlib.Tactic.NoncommRing
/-!
# M-struct... |
spectral.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp.
From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector.
From mathcomp Require Import mxpoly mxred sesqui... |
Cardinal.lean | /-
Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.SetTheory.Cardinal.Finsupp
/-!
# Cardinality of Polynomial Ring
The result in this file is ... |
NonUnitalSubalgebra.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.NonUnitalSubalgebra
import Mathlib.Algebra.Star.StarAlgHom
import Mathlib.Algebra.Star.Center
import Mathlib.Algebra.Star.SelfAdjoint
imp... |
Bousfield.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.Abelian.SerreClass.MorphismProperty
import Mathlib.CategoryTheory.Localization.Bousfield
/-!
# Bousfield localizations with respect to Serre clas... |
Imo1969Q1.lean | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib.Algebra.Ring.Identities
import Mathlib.Data.Int.NatPrime
import Mathlib.Data.Set.Finite.Lemmas
import Mathlib.Tactic.Linarith
/-!
# IMO 1969 Q1
Prove tha... |
Finprod.lean | /-
Copyright (c) 2020 Kexing Ying and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Kevin Buzzard, Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Pi
import Mathlib.Algebra.Group.Indicator
import Mathlib.Algebra.Group.Support
import ... |
Subsingleton.lean | /-
Copyright (c) 2024 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Logic.Basic
/-!
# `subsingleton` tactic
The `subsingleton` tactic closes `Eq` or `HEq` goals using an argument
that the types involved are subsingletons.
T... |
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... |
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 ... |
Basic.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.Algebra.Group.Action.Basic
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.GroupWithZero.Action.H... |
observe.lean | import Mathlib.Data.Nat.Prime.Factorial
import Mathlib.Data.Nat.Factorial.Basic
open Nat
set_option maxHeartbeats 7000 in
theorem euclid (n : ℕ) : ∃ N, n < N ∧ N.Prime := by
let N := n.factorial + 1
let p := minFac N
use p
have prime : p.Prime := by
apply minFac_prime
observe : n.factorial > 0
ome... |
Vector3.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.Fin.Fin2
import Mathlib.Util.Notation3
import Mathlib.Tactic.TypeStar
/-!
# Alternate definition of `Vector` in terms of `Fin2`
This file provid... |
SeparableDegree.lean | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.SplittingField.Construction
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
import Mathlib.FieldTheory.Separable
import Mathlib.FieldTheory.Normal.... |
SeminormFromConst.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
-/
import Mathlib.Analysis.Normed.Unbundled.RingSeminorm
/-!
# SeminormFromConst
In this file, we prove [BGR, Proposition 1.3.2/2][bos... |
CompProd.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.Probability.Kernel.Composition.MapComap
import Mathlib.Probability.Kernel.MeasurableLIntegral
/-!
# Composition-product of kernels
We define the composit... |
inertia.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype div... |
IndYoneda.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.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.CategoryTheory.Limits.Yoneda
/-!
# Ind- and ... |
CountablyGenerated.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
import Mathlib.Order.Filter.AtTopBot.Finite
import Mathlib.Order.Filter.AtTopBot.Prod
import Mathlib.Order.Filter.Coun... |
KummerExtension.lean | /-
Copyright (c) 2023 Andrew Yang, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots
import Mathlib.FieldTheory.Galois.Basic
import Mathlib.FieldTheory.KummerPolynomial
import Mathlib.Linea... |
ssreflect.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Export ssreflect.
Global Set SsrOldRewriteGoalsOrder.
Global Set Asymmetric Patterns.
Global Set Bullet Behavior "None".
#[deprecated(sinc... |
UniformSpace.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Topology.GDelta.MetrizableSpace
import Mathlib.Topology.Separation.GDelta
deprecated_module (since := "2025-05-07")
|
Pi.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
/-!
# Integrability in a product space
We prove that `f : X → Π i, E i` is in `Lᵖ` if and only if ... |
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... |
CartanMatrix.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.Algebra.Lie.Free
import Mathlib.Algebra.Lie.Quotient
import Mathlib.Data.Matrix.Notation
/-!
# Lie algebras from Cartan matrices
Split semi-simple Lie alge... |
ExpGrowth.lean | /-
Copyright (c) 2025 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
import Mathlib.Analysis.Asymptotics.LinearGrowth
import Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp
/-!
# Exponential growth
This file defines the exponenti... |
Star.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.LinearAlgebra.CliffordAlgebra.Conjugation
/-!
# Star structure on `CliffordAlgebra`
This file defines the "clifford conjugation", equal to `reverse (involu... |
Pi.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.Star.Basic
import Mathlib.Algebra.Notation.Pi.Defs
import Mathlib.Algebra.Ring.Pi
/-!
# Basic Results about Star on Pi Types
This file provides bas... |
mxalgebra.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype finfun b... |
IsLocalHomeomorph.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.Topology.PartialHomeomorph
import Mathlib.Topology.SeparatedMap
/-!
# Local homeomorphisms
This file defines local homeomorphisms.
## Main definit... |
RegularSequence.lean | /-
Copyright (c) 2024 Brendan Murphy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Brendan Murphy
-/
import Mathlib.RingTheory.Artinian.Module
import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
import Mathlib.RingTheory.Nakayama
import Mathlib.RingTheory.Regular.... |
all_algebra.v | (* N.B. interval_inference is not exported here.
To enjoys the automation it provides,
you need to explictly "Import interval_inference". *)
From mathcomp Require Export ssralg.
From mathcomp Require Export ssrnum.
From mathcomp Require Export finalg.
From mathcomp Require Export countalg.
From mathcomp Require Export... |
Square.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.MorphismProperty.Limits
import Mathlib.CategoryTheory.Square
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
/-!
# Commutative square... |
Alternating.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Antoine Chambert-Loir
-/
import Mathlib.Algebra.Ring.CharZero
import Mathlib.Data.Fintype.Units
import Mathlib.GroupTheory.IndexNormal
import Mathlib.GroupTheory.Perm.F... |
Splits.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.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Lifts
import Mathlib.Data.List.Prime
import Mathlib.RingTheory.Polynomial.Tower
/-!
# S... |
Filter.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Multiset.MapFold
import Mathlib.Data.Set.Function
import Mathlib.Order.Hom.Basic
/-!
# Filtering multisets by a predicate
## Main definit... |
Thunk.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Init
/-!
# Basic facts about `Thunk`.
-/
namespace Thunk
@[simp] theorem get_pure {α} (x : α) : (Thunk.pure x).get = x := rfl
@[simp] theorem get_mk {α} (... |
KLFun.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
import Mathlib.MeasureTheory.Measure.Decomposition.IntegralRNDeriv
import Mathlib.MeasureTheory.M... |
MooreComplex.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.Homology.HomologicalComplex
import Mathlib.AlgebraicTopology.SimplicialObject.Basic
import Mathlib.CategoryTheory.Abelian.Basic
/-!
## Moore compl... |
ModCases.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth
-/
import Mathlib.Data.Int.ModEq
import Mathlib.Tactic.HaveI
/-! # `mod_cases` tactic
The `mod_cases` tactic does case disjunction on `e % n`, where `... |
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