filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Basic.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.RingTheory.FiniteStability
import Mathlib.RingTheory.Ideal.Quotient.Nilpotent
import Mathlib.RingTheory.Kaehler.Basic
import Mathlib.RingTheory.Localization.... |
Symbols.lean | /-
Copyright (c) 2024 Hannah Fechtner. 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.Data.Finset.Lattice.Lemmas
/-!
# The finite set of symbols in a FreeMonoid element
This is separated from ... |
Normed.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Sébastien Gouëzel, Yury Kudryashov, Dylan MacKenzie, Patrick Massot
-/
import Mathlib.Algebra.BigOperators.Module
import Mathlib.Algebra.Order.Field.Power
import M... |
BigOperators.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.BigOperators.Group.Finset.Preimage
import Mathlib.Order.Filter.AtTopBot.Basic
/-!
# Two lemmas about limit of `Π b ∈ s, f b` along
In this ... |
fingraph.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.
From mathcomp Require Import seq path fintype.
(******************************************... |
Even.lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Equiv.Opposite
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Data.Set.Operations
/-!... |
Finiteness.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.LinearAlgebra.DFinsupp
import Mathlib.RingTheory.Finiteness.Basic
import Mathlib.LinearAlgebra.TensorProduct.Basic
/-!
# Some finiteness results of tensor product
T... |
QuadraticDiscriminant.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.Order.Filter.AtTopBot.Field
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Linarith.Frontend
/-!
# Quadra... |
Sheafify.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.Topology.Sheaves.LocalPredicate
import Mathlib.Topology.Sheaves.Stalks
/-!
# Sheafification of `Type` valued presheaves
We construct the sheafification o... |
Instances.lean | /-
Copyright (c) 2025 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Patrick Massot, Anatole Dedecker
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Order.Filter.IsBounded
import Mat... |
Attr.lean | /-
Copyright (c) 2024 Tomáš Skřivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomáš Skřivan
-/
import Mathlib.Tactic.FunProp.Decl
import Mathlib.Tactic.FunProp.Theorems
/-!
## `funProp` attribute
-/
namespace Mathlib
open Lean Meta
namespace Meta.FunProp
priv... |
binomial.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 fintype tuple ... |
Variables.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import Mathlib.Data.Finsupp.Lex
import Mathlib.Algebra.MvPolynomial.Degrees
/-!
# Variables of polynomials
This file establishes man... |
Sublocale.lean | /-
Copyright (c) 2025 Christian Krause. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chriara Cimino, Christian Krause
-/
import Mathlib.Order.Nucleus
import Mathlib.Order.SupClosed
/-!
# Sublocale
Locales are the dual concept to frames. Locale theory is a branch of... |
Dual.lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
import Mathlib.Analysis.Normed.Group.NullSubmodule
import Mathlib.Topology.Algebra.Module.PerfectPair... |
AkraBazzi.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.SumTransform
import Mathlib.Analysis.Calculus.Deriv.Inv
import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
/-!
# Divide-and... |
AlgebraicClosure.lean | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.FieldTheory.AlgebraicClosure
import Mathlib.RingTheory.Algebraic.Integral
import Mathlib.RingTheory.AlgebraicIndependent.Transcendental
/-!
# Algebraic independ... |
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
-/
import Mathlib.GroupTheory.Subsemigroup.Centralizer
import Mathlib.GroupTheory.Submonoid.Center
/-!
# Centralizers of magmas and monoids
## Main definitions
* `S... |
FintypeCat.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Adam Topaz
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Endomorphism
import Mathlib.CategoryTheory.Skeletal
import Mathlib.Data.Finit... |
AddSub.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.Count
import Mathlib.Data.List.Count
/-!
# Sum and difference of multisets
This file defines the following operations on multise... |
OfColimitCommutesFiniteLimit.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.Types.Colimits
import Mathlib.CategoryTheory.Limits.Filtered
import Mathlib.CategoryTheory.Limits.Yoneda
/-!
# If colimits of shap... |
enat_to_nat.lean | import Mathlib.Tactic.ENatToNat
example (a b : ENat) (h : a = b) : a - b = b - a := by
enat_to_nat
omega
example (a b : ENat) (h : a ≤ b) : a - b < b + 1 := by
enat_to_nat
omega
example (a b : ENat) (h : a ≤ b) : a - 2 * b ≤ b + 1 := by
enat_to_nat
omega
example (a b c : ENat) (hab : a ≥ b) (hbc : b ≥ c... |
MinMax.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.Logic.OpClass
import Mathlib.Order.Lattice
/-!
# `max` and `min`
This file proves basic properties about maxima and minima on a `LinearOrder`.
## Ta... |
ExistsI.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Tactic.ExistsI
example : ∃ x : Nat, x = x := by
existsi 42
rfl
example : ∃ x : Nat, ∃ y : Nat, x = y := by
existsi 42, 42
rfl
|
UniversalVerts.lean | /-
Copyright (c) 2024 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Otte
-/
import Mathlib.Combinatorics.SimpleGraph.Clique
import Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents
import Mathlib.Combinatorics.SimpleGraph.Matching
/-!
# Universa... |
FromLRAT.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Group.Nat.Defs
import Mathlib.Tactic.ByContra
/-!
# `lrat_proof` command
Defines a macro for producing SAT proofs from CNF / LRAT files.
Thes... |
Defs.lean | /-
Copyright (c) 2021 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
import Mathlib.LinearAlgebra.GeneralLinearGroup
import M... |
Basic.lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yury Kudryashov, Joseph Myers, Heather Macbeth, Kim Morrison, Yaël Dillies
-/
import Mathlib.Algebra.GroupWithZero.Action.Units
import Mathlib.Algebra.Module.End
import ... |
center.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import fintype bigop finset fingroup morphism perm.
From math... |
Finite.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.LinearAlgebra.FreeModule.PID
import Mathlib.LinearAlgebra.Matrix.AbsoluteValue
import Mathlib.NumberTheory.... |
qfpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple div bigop binomial finset finfun.
From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm.
From mathcomp Require Import fingroup falgebra fiel... |
CharZero.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.Algebra.Notation.Support
import Mathlib.Algebra.Ring.Units
import Mathlib.Data.Nat.Cast.Basic
import M... |
Invariant.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Module.Equiv.Basic
import Mathlib.Algebra.Module.Submodule.Map
import Mathlib.LinearAlgebra.Span.Defs
import Mathlib.Order.Sublattice
/-!
# The latt... |
TransImports.lean | import Mathlib.Util.TransImports
/--
info: 'MathlibTest.TransImports' has at most 1000 transitive imports
2 starting with "Mathlib.Tactic.Linter.H":
[Mathlib.Tactic.Linter.HashCommandLinter, Mathlib.Tactic.Linter.Header]
-/
#guard_msgs in
#trans_imports "Mathlib.Tactic.Linter.H" at_most 1000
|
Nondegenerate.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.Adjugate
/-!
# Matrices associated with non-dege... |
Int.lean | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Algebra.Field.ZMod
import Mathlib.RingTheory.Ideal.Norm.AbsNorm
/-!
# Ideal of `ℤ`
We prove results about ideals of `ℤ` or ideals of extensions of `ℤ`.... |
Infinite.lean | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Data.Set.Finite.Basic
import Mathlib.Order.Interval.Set.Basic
/-!
# Infinitude of intervals
Bounded intervals in dense orders are infinite, as are unbounde... |
Final.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.Functor.KanExtension.Adjunction
import Mathlib.CategoryTheory.Limits.IsConnected
import Mathlib.CategoryTheory.Limits.Sifted
import ... |
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.Algebra.Homology.HomotopyCategory.HomologicalFunctor
import Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence
import Mathlib.Algebra.Homology.HomotopyCateg... |
lint-style.lean | /-
Copyright (c) 2024 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
import Lake.CLI.Main
import Lean.Elab.ParseImportsFast
import Batteries.Data.String.Basic
import Mathlib.Tactic.Linter.TextBased
import Cli.Basic
/-!
# Text-bas... |
OrderedMonoid.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Abhimanyu Pallavi Sudhir
-/
import Mathlib.Algebra.Module.Pi
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Order.Filter.Germ.Basic
/-!
# Ordered ... |
UniqueDifferential.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import Mathlib.Geometry.Manifold.MFDeriv.Atlas
import Mathlib.Geometry.Manifold.VectorBundle.Basic
/-!
# Unique derivative sets in manifolds
... |
Quotient.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.Algebra.Field.Basic
import Mathlib.Algebra.Order.Group.Unbundled.Int
import Mathlib.Algebra.Module.NatInt
import Mathlib.GroupTheory.QuotientGroup.Defs
impor... |
PUnit.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.Module.Defs
import Mathlib.Algebra.Ring.Action.Basic
import Mathlib.Algebra.Ring.PUnit
/-!
# Instances on PUnit
This file collects facts about module s... |
Pullback.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.Generator
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward
import Mathlib.CategoryTheory.Adjunction.PartialAdjo... |
StrongRankCondition.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.RingTheory.FiniteType
import Mathlib.LinearAlgebra.InvariantBasisNumber
/-!
# Strong rank condition for commutative rings
We prove that any nontri... |
Principal.lean | /-
Copyright (c) 2022 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.Ordinal.FixedPoint
/-!
# Principal ordinals
We define principal or indecomposable ordinals, and we prove the standa... |
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... |
mxpoly.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import div fintype tupl... |
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... |
HomologicalComplexAbelian.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.Additive
import Mathlib.Algebra.Homology.HomologicalComplexLimits
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
/-! # THe category of... |
KummerPolynomial.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.AdjoinRoot
import Mathlib.RingTheory.Norm.Defs
/-!
# Irreducibility of X ^ p - a
## Main result
- `X_pow_sub_C_irreducible_iff_of_p... |
Centroid.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.LinearAlgebra.AffineSpace.Combination
/-!
# Centroid of a Finite Set of Points in Affine Space
This file defines the centroid of a finite set of points i... |
Homology.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Richard Hill, Andrew Yang
-/
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algebra.Category.ModuleCat.Topology.Basic
import Mathlib.Algebra.Homology.ShortComplex.Abelia... |
apply_with.lean | import Mathlib.Tactic.ApplyWith
set_option autoImplicit true
example (f : ∀ x : Nat, x = x → α) : α := by
apply (config := {}) f
apply rfl
apply 1
example (f : ∀ x : Nat, x = x → α) : α := by
apply (config := { newGoals := .nonDependentOnly }) f
apply @rfl _ 1
example (f : ∀ x : Nat, x = x → α) : α := by
... |
AddAut.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.GroupWithZero.Action.Basic
import Mathlib.Algebra.GroupWithZero.Action.Units
import Mathlib.Algebra.Group.Units.Opposite
import Mathlib.Algeb... |
Functorial.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.Functor.Basic
/-!
# Unbundled functors, as a typeclass decorating the object-level function.
-/
namespace CategoryTheory
-- declare the ... |
FinsetBuilder.lean | import Mathlib.Data.Fintype.Defs
variable {α : Type*} [Fintype α] {p : α → Prop} {s : Finset α} {a : α}
[DecidablePred p] [DecidableEq α] [Singleton α (Finset α)] [HasCompl (Finset α)]
/-- info: {x | p x} : Finset α -/
#guard_msgs in
#check ({x | p x} : Finset α)
/-- info: {x ∈ s | p x} : Finset α -/
#guard_msgs... |
LibraryRewrite.lean | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid, Anand Rao
-/
import Mathlib.Lean.Meta.RefinedDiscrTree
import Mathlib.Tactic.Widget.InteractiveUnfold
import ProofWidgets.Component.FilterDetails
/-!
# Point & cli... |
Basic.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib.Algebra.AddTorsor.Defs
import Mathlib.Algebra.Group.Action.Basic
import Mathlib.Algebra.Group.End
import Mathlib.Algebra.Group.Pointwise.S... |
Hom.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov, Amelia Livingston
-/
import Mathlib.RingTheory.Coalgebra.Basic
/-!
# Homomorphisms of `R`-coalgebras
This file defines bundled homomorphisms of `R`-coa... |
Option.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.Data.Fintype.Option
import Mathlib.GroupTheory.Perm.Sign
/-!
# Permutations of `Option α`
-/
open Equiv
@[simp]
theorem Equiv.optionCongr_one {α : Type*}... |
Option.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.Algebra.Group.Action.Faithful
/-!
# Option instances for additive and multiplicative actions
This file defines instances for additive and multiplicative ... |
Germ.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
import Mathlib.Algebra.Module.LinearMap.Defs
import Mathlib.Algebra.Order.Hom.Ring
import Mathlib.Order.Filter.G... |
ToNat.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.SetTheory.Cardinal.ENat
/-!
# Projection from cardinal numbers to natural numbers
In this file we define `Cardinal.toNat` to be the natural projectio... |
Transfer.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Abelian.Basic
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages
import Mat... |
Prod.lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.MeasureTheory.Measure.GiryMonad
import Mathlib.MeasureTheory.Measure.OpenPos
/-!
# The product measure
In this file we define and prove propertie... |
Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Lemmas
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algebra.BigOperators.Group... |
Projections.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Faces
import Mathlib.CategoryTheory.Idempotents.Basic
/-!
# Construction of projections for the Dold-Kan correspondence
In this file... |
Basic.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.Category.Ring.Colimits
import Mathlib.Algebra.Category.Ring.Constructions
import Mathlib.CategoryTheory.Comma.Over.Pullback
/-!
# Under `C... |
generic_quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice.
From mathcomp Require Import seq fintype.
(*****... |
Basic.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.Algebra.Order.Floor.Defs
import Mathlib.Algebra.Order.Floor.Semiring
import Mathlib.Combinatorics.SimpleGraph.Operations
import Mathlib.Combinatorics... |
Jensen.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Function
import Mathlib.Tactic.FieldSimp
/-!
# Jensen's inequality... |
Shrink.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.Group.Shrink
import Mathlib.Algebra.Module.TransferInstance
/-!
# Transfer module and algebra structures from `α` to `Shrink α`
-/
-- FIXME: `to_... |
StoneCech.lean | import Mathlib.Topology.Compactification.StoneCech
deprecated_module (since := "2025-06-07")
|
fintype.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 ssrnotations eqtype.
From mathcomp Require Import ssrnat seq choice pat... |
Univ.lean | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
import Mathlib.RingTheory.MvPolynomial.Homogeneous
/-!
# The universal c... |
Finite.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.RingTheory.LocalProperties.Basic
import Mathlib.RingTheory.Localization.Integer
import Mathlib.RingTheory.TensorProduct.Finite
/-!
# The meta properties of... |
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... |
Basic.lean | /-
Copyright (c) 2023 Ziyu Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ziyu Wang, Chenyi Li, Sébastien Gouëzel, Penghao Yu, Zhipeng Cao
-/
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.Calculus.FDeriv.Basic
import Mathlib.Analysis.Calc... |
IrrationalPowerOfIrrational.lean | /-
Copyright (c) 2024 Seewoo Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seewoo Lee
-/
import Mathlib.Data.Real.Irrational
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
/-
# Irrational power of irrational numbers are not necessarily irrational.
Prove th... |
Periodic.lean | /-
Copyright (c) 2021 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
import Mathlib.Algebra.Ring.Periodic
import Mathlib.Data.Nat.Count
/-!
# Periodic Functions on ℕ
This file identifies a few functions on `ℕ` which are periodic, and a... |
Assoc.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting
/-!
# Associativity of pullbacks
This file shows that pullbacks (and pushouts) are associative up to natura... |
Equivalence.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.ModelTheory.Satisfiability
/-!
# Equivalence of Formulas
## Main Definitions
- `FirstOrder.Language.Theory.Imp`: `φ ⟹[T] ψ` indicates that `φ` implie... |
choice.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(**************************************************... |
FiberPartition.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.Data.Set.Insert
/-!
This file defines the type `f.Fiber` of fibers of a function `f : Y → Z`, and provides some API
to work with and construct ter... |
LiminfLimsup.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Algebra.Order.Group.DenselyOrdered
import Mathlib.Data.Real.Archimedean
import Mathlib.Topology.Algebra.... |
SFinite.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.Typeclasses.Finite
/-!
# Classes for s-finite measures
We introduce the following typeclasses for measures:
* ... |
CategoryWithCofibrations.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.Basic
/-!
# Categories with classes of fibrations, cofibrations, weak equivalences
We introduce typeclasses `CategoryWithFibrat... |
Defs.lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.RingTheory.Ideal.Maximal
/-!
# Maximal spectrum of a commutative (semi)ring
The maximal spectrum of a commutative (semi)ring is t... |
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... |
Symmetric.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.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric
/-!
# The monoidal structure on `Quadra... |
Cocardinal.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.Order.Filter.Cofinite
import Mathlib.Order.Filter.CountableInter
import Mathlib.Order.Filter.CardinalInter
import Mathlib.SetTheory.Cardinal.Arithmetic
imp... |
UniformTime.lean | /-
Copyright (c) 2023 Winston Yin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Winston Yin
-/
import Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique
/-!
# Uniform time lemma for the global existence of integral curves
## Main results
* `exists_isMIntegralCurv... |
PresheafOfFunctions.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.Topology.Sheaves.Presheaf
/-!
# Presheaves of functions
We construct some simple examples of presheaves of functions on a topological space.
* `presheafTo... |
ExtensiveSheaves.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Sites.Canonical
import Mathlib.Category... |
Schreier.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.Group.Pointwise.Finset.Basic
import Mathlib.GroupTheory.Abelianization.Defs
import Mathlib.GroupTheory.Commutator.Finite
import Mathlib.Group... |
FunProp.lean | /-
Copyright (c) 2024 Tomas Skrivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomas Skrivan
-/
import Mathlib.Tactic.FunProp.Attr
import Mathlib.Tactic.FunProp.Core
import Mathlib.Tactic.FunProp.Decl
import Mathlib.Tactic.FunProp.Elab
import Mathlib.Tactic.FunPro... |
Finite.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
-/
import Mathlib.Data.Set.Finite.Lattice
import Mathlib.Order.Filter.Basic
/-!
# Results filters related to finiteness.
-/
open Function Set Order
o... |
ValExtension.lean | /-
Copyright (c) 2024 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang, Bichang Lei
-/
import Mathlib.RingTheory.Valuation.Extension
deprecated_module (since := "2025-05-06")
|
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