filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Preadditive.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.Group.TransferInstance
import Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions
import Mathlib.CategoryTheory.Localization.HasLocalizatio... |
CollectFacts.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.Order.BoundedOrder.Basic
import Mathlib.Order.Lattice
import Qq
/-!
# Facts collection for the `order` Tactic
This file implements the collection... |
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, Jireh Loreaux
-/
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.Ring.Defs
import Mathlib.Algebra.Ring.Basic
/-!
# Homomorphisms of semirings and... |
Hom.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.Topology.Algebra.ContinuousMonoidHom
import Mathlib.Topology.Algebra.SeparationQuotient.Basic
/-!
# Lift of `MonoidHom M N` to `MonoidHom (SeparationQuoti... |
DifferentialObject.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.Group.Basic
import Mathlib.Data.Int.Cast.Defs
import Mathlib.CategoryTheory.Shift.Basic
import Mathlib.CategoryTheory.ConcreteCategory.Basic
/-!
#... |
Irrational.lean | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
import Mathlib.Data.Real.Irrational
import Mathlib.Topology.Algebra.Order.Floor
/-!
# `Real.pi` is irrational
T... |
Compare.lean | /-
Copyright (c) 2024 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Tactic.Ring.Basic
import Mathlib.Tactic.NormNum.Ineq
/-!
# Automation for proving inequalities in commutative (semi)rings
This file provides automa... |
Paracompact.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.Tactic.GCongr
import Mathlib.Topology.Compactness.Paracompact
import Mathlib.Topology.EMetricSpace.Basic
import Mathlib.SetTheory.Cardinal.Order
/-!... |
Sym2.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.Algebra.Group.Action.Pi
import Mathlib.Data.Finset.Prod
import Mathlib.Data.SetLike.Basic
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Sym2.Init
/-... |
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... |
countalg.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 ss... |
ContinuousMapZero.lean | /-
Copyright (c) 2025 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.ContinuousMap.ContinuousMapZero
import Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap
/-!
# Specific results about `ContinuousMapZ... |
Card.lean | /-
Copyright (c) 2025 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.BigOperators.Finprod
import Mathlib.Data.Set.Card
import Mathlib.Data.Setoid.Partition
/-! # Cardinality of parts of partitions... |
Instances.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.Algebra.Category.Ring.Basic
import Mathlib.RingTheory.Localization.Away.Basic
import Mathlib.RingTheory.LocalRing.RingHom.Basic
/-!
# Ring-theoretic results... |
Basic.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.Kaehler.Polynomial
import Mathlib.Algebra.Module.FinitePresentation
import Mathlib.RingTheory.Extension.Presentation.Basic
/-!
# Naive cotangent... |
Basic.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, Jean Lo, Calle Sönne
-/
import Mathlib.Analysis.SpecialFunctions.Exp
import Mathlib.Data.Nat.Factorization.Defs
import Mathlib.Analysis.NormedSpac... |
HigherOrder.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 Lean.Elab.Term
import Lean.Meta.Tactic.Apply
import Lean.Meta.Tactic.Assumption
import Lean.Meta.MatchUtil
import Lean.Meta.Tactic.Intro
import Lean.Elab.Declaration... |
Shift.lean | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Yaël Dillies
-/
import Mathlib.Analysis.Calculus.Deriv.Add
import Mathlib.Analysis.Calculus.Deriv.Comp
import Mathlib.Analysis.Calculus.Deriv.CompMul
/-!
### Invariance ... |
Orthogonal.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Subspace
import Mathlib.LinearAlgebra.SesquilinearForm
/-!
# Orthogonal complements of su... |
Gamma.lean | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
import Mathlib.Probability.Notation
import Mathlib.Probability.CDF
import Mathlib.Analysis.SpecialFunctions.Gamma.Basic
/-! # Gamma distributions over ℝ
Define the gamm... |
Holder.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.MetricSpace.Lipschitz
import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
/-!
# Hölder continuous functions
In this file we define Höl... |
Reflection.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.Data.Matrix.Notation
import Mathlib.Data.Fin.Tuple.Reflection
/-!
# Lemmas for concrete matrices `Matrix (Fin m) (Fin n) α`
This file contains alternative ... |
Represents.lean | /-
Copyright (c) 2025 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Otte
-/
import Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting
import Mathlib.Data.Set.Card
/-!
# Representation of components by a set of vertices
## Main definition
* `... |
Opposite.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Module.Equiv.Defs
import Mathlib.Algebra.Module.Opposite
/-!
# Module operations on `Mᵐᵒᵖ`
This file contains definitions that build on top of the ... |
Completion.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin
-/
import Mathlib.Analysis.Normed.Group.SemiNormedGrp
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.Analysis.Normed.Group.Ho... |
FiniteDimensional.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn
import Mathlib.Analysis.Normed.Module.FiniteDimension
/-!
# A lemma about `Approxi... |
Units.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Ring.Int.Units
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Fintype.Sum
import Mathlib.SetTheory.Cardinal.Finite
import Mathlib.Algebra... |
IsPrimary.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yakov Pechersky
-/
import Mathlib.RingTheory.IsPrimary
import Mathlib.RingTheory.Ideal.Operations
/-!
# Primary ideals
A proper ideal `I` is primary iff `xy ∈ I` implies `x ∈ I... |
Defs.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.Polynomial.AlgebraMap
/-!
# Algebraic elements and algebraic extensions
An element of an R-algebra is algebraic over R if it is the root of a... |
Cardinality.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, Alexander Bentkamp, Kim Morrison
-/
import Mathlib.LinearAlgebra.Basis.Defs
import Mathlib.LinearAlgebra.LinearIndependent.Defs
import Mathlib.LinearAlg... |
tuple.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat.
From mathcomp Require Import seq choice fintype path.
S... |
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... |
quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype prim... |
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... |
Monad.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 Mathlib.Init
/-!
# Monad instances for `List`
-/
universe u
namespace List
variable {α : Type u}
instance instMonad : Monad List.{u} where
pur... |
Basic.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Thomas Murrills
-/
import Mathlib.Algebra.GroupWithZero.Invertible
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Data.Nat.Cast.Basic
import Mathlib.Data.Nat.Cast.... |
ConformalLinearMap.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Normed.Operator.LinearIsometry
import Mathlib.LinearAlgebra.Basis.VectorSpace
/-!
# Conformal Linear ... |
UV.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Combinatorics.SetFamily.Shadow
/-!
# UV-compressions
This file defines UV-compression. It is an operation on a set family that reduces its ... |
StrictConvexBetween.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Analysis.Convex.Between
import Mathlib.Analysis.Convex.StrictConvexSpace
import Mathlib.Analysis.Normed.Affine.AddTorsor
import Mathlib.Analysis.Normed.Aff... |
StdBasis.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Algebra.Pi
import Mathlib.LinearAlgebra.Finsupp.VectorSpace
import Mathlib.LinearAlgebra.FreeModule.Basic
import Mathlib.LinearAlgebra.LinearIn... |
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.Group.Prod
import Mathlib.Algebra.Order.Group.Synonym
import Mathlib.Algebra.Order.Monoid.Cano... |
Subcategory.lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Linear
import Mathlib.CategoryTheory.Monoidal.Transport
import Mathlib.C... |
Finsupp.lean | /-
Copyright (c) 2025 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Algebra.GroupWithZero.Basic
import Mathlib.Data.Finset.Sym
import Mathlib.Data.Finsupp.Defs
/-!
# Finitely supported functions from the symmet... |
all_order.v | Require Export order.
|
Choose.lean | /-
Copyright (c) 2025 Mitchell Horner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Horner
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
import Mathlib.Data.Nat.Cast.Field
/-!
# Binomial coefficient... |
PositiveLinearMap.lean | /-
Copyright (c) 2025 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Algebra.Module.LinearMap.Defs
import Mathlib.Algebra.Order.Hom.Monoid
import Mathlib.Tactic.ContinuousFunctionalCalculus
/-! # Positive linear maps... |
classfun.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... |
WithTop.lean | /-
Copyright (c) 2024 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yaël Dillies
-/
import Mathlib.Algebra.Order.Ring.WithTop
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Sums in `WithTop`
This file proves results about ... |
ValuativeRel.lean | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.NumberTheory.Padics.PadicNumbers
import Mathlib.RingTheory.Valuation.RankOne
/-!
# p-adic numbers with a valuative relation
## Tags
p-adic, p adic... |
ENat.lean | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.ENat.Lattice
import Mathlib.Data.Matroid.Rank.Finite
import Mathlib.Data.Matroid.Loop
import Mathlib.Tactic.TautoSet
/-!
# `ℕ∞`-valued rank
If the '... |
Constructions.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.Data.Finset.Insert
import Mathlib.Data.Set.Lattice
/-!
# Constructions involving sets of sets.
## Finite Intersections
We define a structure `FiniteInter` w... |
mxabelem.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... |
Zero.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.Jacobson.Ring
import Mathlib.RingTheory.Spectrum.Prime.Topology
/-!
# Zero-dimensional rings
We provide further API for zero-dimensional rings.... |
Pi.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.Idempotents
import Mathlib.RingTheory.Smooth.Basic
/-!
# Formal-smoothness of finite products of rings
## Main result
- `Algebra.FormallySmoot... |
algebraize.lean | import Mathlib.Tactic.Algebraize
set_option linter.unusedVariables false
section example_definitions
/-- Test property for when `RingHom` and `Algebra` properties are definitionally the same,
see e.g. `RingHom.FiniteType` for a concrete example of this. -/
class Algebra.TestProperty1 (A B : Type*) [CommRing A] [Comm... |
ExtendDoc.lean | /-
Copyright (c) 2023 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Init
import Lean.Elab.ElabRules
import Lean.DocString
/-!
# `extend_doc` command
In a file where declaration `decl` is defined, writing
```lean
exten... |
Algebra.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Algebra.Module.LocalizedModule.IsLocalization
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Localization.BaseChange
import Mathlib... |
Range.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.UnionInter
/-! # `Multiset.range n` gives `{0, 1, ..., n-1}` as a multiset. -/
assert_not_exists Monoid
open List Nat
namespac... |
Elementwise.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.Tactic.CategoryTheory.Elementwise
import Mathlib.CategoryTheory.ConcreteCategory.Basic
/-!
# Use the `elementwise` attribute to create applied versions of... |
ssrnat.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Import PosDef.
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype.
#[export] Set Warnings "-ov... |
Lipschitz.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.Algebra.Order.Field
import Mathlib.Topology.MetricSpace.Lipschitz
/-!
# Lipschitz continuous functions
This file develops Lipschitz co... |
Subgraph.lean | /-
Copyright (c) 2023 Kyle Miller, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Rémi Bottinelli
-/
import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
import Mathlib.Data.Set.Card
/-!
# Connectivity of subgraphs and induced ... |
Defs.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.Order.Interval.Finset.Basic
import Mathlib.Combinatorics.Additive.Frei... |
Constructions.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Algebra.Group.PUnit
import Mathlib.Algebra.Group.ULift
import Mathlib.Analysis.Normed.Group.Basic
/-!
# Product of norme... |
Associated.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.GroupWithZero.Associated
import Mathlib.Algebra.Ring.Int.Units
/-!
# Associated elements and the integers
This file contains some results on equalit... |
Subgraph.lean | /-
Copyright (c) 2021 Hunter Monroe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hunter Monroe, Kyle Miller, Alena Gusakov
-/
import Mathlib.Combinatorics.SimpleGraph.DeleteEdges
import Mathlib.Data.Fintype.Powerset
/-!
# Subgraphs of a simple graph
A subgraph of ... |
Interval.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
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Pointwise.Set.Scalar
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.A... |
ProductMeasure.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.Probability.Kernel.Composition.MeasureComp
import Mathlib.Probability.Kernel.IonescuTulcea.Traj
/-!
# Infinite product of probability measures
This f... |
Basic.lean | /-
Copyright (c) 2023 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Homology.Opposite
import Mathlib.Algebra.Homology.ConcreteCategory
import Mathlib.RepresentationTheory.Homological.Resolution
import Math... |
Laplacian.lean | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
import Mathlib.Analysis.Calculus.ContDiff.Basic
import Mathlib.Analysis.Calculus.ContDiff.Operations
import Mathlib.Analysis.InnerProductSpace.CanonicalTensor
/-!
# ... |
tuple.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat.
From mathcomp Require Import seq choice fintype path.
S... |
matrix.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 f... |
Ideal.lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Logic.Encodable.Basic
import Mathlib.Order.Atoms
import Mathlib.Order.Cofinal
import Mathlib.Order.UpperLower.Principal... |
EffectiveEpi.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.EffectiveEpi.RegularEpi
import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
/-!
# Effective epimorphisms in `TopCat`
This fil... |
Cardinal.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Floris Van Doorn
-/
import Mathlib.Algebra.CharZero.Infinite
import Mathlib.Algebra.Ring.Rat
import Mathlib.Data.Rat.Encodable
import Mathlib.SetTheory.Cardinal.Basic
/-!
... |
LocalAtTarget.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.Homeomorph.Lemmas
import Mathlib.Topology.Sets.OpenCover
import Mathlib.Topology.LocallyClosed
/-!
# Properties of maps that are local at the targe... |
commutator.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 fintype.
From mathcomp Require Import bigop finset binomial fingroup morphism.
From mathcomp... |
HigherOrder.lean | import Mathlib.Tactic.HigherOrder
set_option autoImplicit true
namespace HigherOrderTest
@[higher_order map_comp_pure]
theorem map_pure' {f : Type u → Type v} [Applicative f] [LawfulApplicative f]
{α β : Type u} (g : α → β) (x : α) : g <$> (pure x : f α) = pure (g x) := map_pure g x
example {f : Type u → Type v} [... |
Basic.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.Kernel.Defs
/-!
# Basic kernels
This file contains basic results about kernels in general and definitions of some particular
kernels.
## Mai... |
Extended.lean | /-
Copyright (c) 2024 James Sundstrom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: James Sundstrom
-/
import Mathlib.RingTheory.FractionalIdeal.Basic
/-!
# Extension of fractional ideals
This file defines the extension of a fractional ideal along a ring homomorphi... |
Lemmas.lean | /-
Copyright (c) 2021 Chris Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Bailey
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Data.String.Defs
import Mathlib.Tactic.Basic
import Batteries.Tactic.Alias
/-!
# Miscellaneous lemmas about strings
-/
n... |
Basic.lean | /-
Copyright (c) 2024. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hannah Fechtner
-/
import Mathlib.Algebra.FreeMonoid.Basic
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.GroupTheory.Congruence.Hom
/-!
# Defining a monoid given by generators an... |
FiniteProducts.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# Categories with finite (co)products
Typeclasses repr... |
Image.lean | /-
Copyright (c) 2017 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov, Paul Lezeau
-/
import Mathlib.Data.Set.NAry
import Mathlib.Order.Bounds.Basic
/-!
# Images of upper/lower bounds under monotone functions
In this file ... |
Pullbacks.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.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.H... |
ConformalLinearMap.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import Mathlib.Analysis.NormedSpace.ConformalLinearMap
import Mathlib.Analysis.InnerProductSpace.LinearMap
/-!
# Conformal maps between inner product spaces
In an inner... |
LocallyDiscrete.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.Discrete.Basic
import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
import Mathlib.CategoryTheory.Bicategory.Strict
/-!
# Loc... |
LocalSubring.lean | /-
Copyright (c) 2024 Andrew Yang, Yaël Dillies, Javier López-Contreras. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Yaël Dillies, Javier López-Contreras
-/
import Mathlib.Tactic.FieldSimp
import Mathlib.RingTheory.LocalRing.RingHom.Basic
import Mathlib... |
Exponent.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Algebra.GCDMonoid.Finset
import Mathlib.Algebra.GCDMonoid.Nat
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Data.Nat.Fac... |
ssralg.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 choice fintype finf... |
zmodp.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 choice eqtype ssrnat seq.
From mathcomp Require Import div fintype bigo... |
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 ... |
Grp_.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.Monoidal.Internal.Types.Basic
import Mathlib.CategoryTheory.Monoidal.Grp_
import Mathlib.Algebra.Category.Grp.Basic
/-!
# `Grp_ (Type u) ... |
TransfiniteIteration.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Violeta Hernández Palacios
-/
import Mathlib.Order.SuccPred.Limit
/-!
# Transfinite iteration of a function `I → I`
Given `φ : I → I` where `[SupSet I]`, we define the `j`th t... |
fingroup.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 div path... |
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... |
extremal.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... |
RingNF.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Anne Baanen
-/
import Mathlib.Tactic.Ring.Basic
import Mathlib.Tactic.TryThis
import Mathlib.Tactic.Conv
import Mathlib.Util.AtomM.Recurse
import Mathlib.Util.Qq
/-!
#... |
ULift.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.ULift
import Mathlib.Algebra.Ring.ULift
/-!
# Field instances for `ULift`
This file defines insta... |
Integral.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.Analysis.Convex.Function
import Mathlib.Analysis.Convex.StrictConvexSpace
import Mathlib.MeasureTheory.Function.AEEqOfIntegral
import Mathlib.Measure... |
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